Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,7,Mod(8,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.8");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.83113575602\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 642x^{10} + 155265x^{8} + 17813036x^{6} + 1003321428x^{4} + 26369892864x^{2} + 256461520896 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{8}\cdot 7^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 8.8 | ||
Root | \(5.92187i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.8 |
Dual form | 21.7.b.a.8.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.92187i | 0.740234i | 0.928985 | + | 0.370117i | \(0.120682\pi\) | ||||
−0.928985 | + | 0.370117i | \(0.879318\pi\) | |||||||
\(3\) | 25.5592 | − | 8.70200i | 0.946639 | − | 0.322296i | ||||
\(4\) | 28.9315 | 0.452054 | ||||||||
\(5\) | − | 144.537i | − | 1.15630i | −0.815932 | − | 0.578148i | \(-0.803776\pi\) | ||
0.815932 | − | 0.578148i | \(-0.196224\pi\) | |||||||
\(6\) | 51.5321 | + | 151.359i | 0.238575 | + | 0.700734i | ||||
\(7\) | 129.642 | 0.377964 | ||||||||
\(8\) | 550.328i | 1.07486i | ||||||||
\(9\) | 577.550 | − | 444.833i | 0.792250 | − | 0.610196i | ||||
\(10\) | 855.929 | 0.855929 | ||||||||
\(11\) | 1762.28i | 1.32402i | 0.749493 | + | 0.662012i | \(0.230297\pi\) | ||||
−0.749493 | + | 0.662012i | \(0.769703\pi\) | |||||||
\(12\) | 739.466 | − | 251.762i | 0.427932 | − | 0.145695i | ||||
\(13\) | −1258.93 | −0.573021 | −0.286510 | − | 0.958077i | \(-0.592495\pi\) | ||||
−0.286510 | + | 0.958077i | \(0.592495\pi\) | |||||||
\(14\) | 767.722i | 0.279782i | ||||||||
\(15\) | −1257.76 | − | 3694.26i | −0.372670 | − | 1.09459i | ||||
\(16\) | −1407.36 | −0.343593 | ||||||||
\(17\) | − | 6025.19i | − | 1.22638i | −0.789936 | − | 0.613189i | \(-0.789886\pi\) | ||
0.789936 | − | 0.613189i | \(-0.210114\pi\) | |||||||
\(18\) | 2634.24 | + | 3420.18i | 0.451688 | + | 0.586450i | ||||
\(19\) | −9374.79 | −1.36679 | −0.683393 | − | 0.730051i | \(-0.739496\pi\) | ||||
−0.683393 | + | 0.730051i | \(0.739496\pi\) | |||||||
\(20\) | − | 4181.67i | − | 0.522708i | ||||||
\(21\) | 3313.55 | − | 1128.14i | 0.357796 | − | 0.121817i | ||||
\(22\) | −10436.0 | −0.980087 | ||||||||
\(23\) | 15380.6i | 1.26413i | 0.774916 | + | 0.632064i | \(0.217792\pi\) | ||||
−0.774916 | + | 0.632064i | \(0.782208\pi\) | |||||||
\(24\) | 4788.95 | + | 14066.0i | 0.346423 | + | 1.01750i | ||||
\(25\) | −5265.94 | −0.337020 | ||||||||
\(26\) | − | 7455.20i | − | 0.424169i | ||||||
\(27\) | 10890.8 | − | 16395.4i | 0.553311 | − | 0.832975i | ||||
\(28\) | 3750.73 | 0.170860 | ||||||||
\(29\) | − | 17060.6i | − | 0.699520i | −0.936839 | − | 0.349760i | \(-0.886263\pi\) | ||
0.936839 | − | 0.349760i | \(-0.113737\pi\) | |||||||
\(30\) | 21876.9 | − | 7448.29i | 0.810256 | − | 0.275863i | ||||
\(31\) | −20504.9 | −0.688292 | −0.344146 | − | 0.938916i | \(-0.611832\pi\) | ||||
−0.344146 | + | 0.938916i | \(0.611832\pi\) | |||||||
\(32\) | 26886.8i | 0.820520i | ||||||||
\(33\) | 15335.3 | + | 45042.5i | 0.426728 | + | 1.25337i | ||||
\(34\) | 35680.4 | 0.907806 | ||||||||
\(35\) | − | 18738.0i | − | 0.437039i | ||||||
\(36\) | 16709.4 | − | 12869.7i | 0.358140 | − | 0.275842i | ||||
\(37\) | 8468.56 | 0.167188 | 0.0835939 | − | 0.996500i | \(-0.473360\pi\) | ||||
0.0835939 | + | 0.996500i | \(0.473360\pi\) | |||||||
\(38\) | − | 55516.3i | − | 1.01174i | ||||||
\(39\) | −32177.2 | + | 10955.2i | −0.542444 | + | 0.184682i | ||||
\(40\) | 79542.7 | 1.24286 | ||||||||
\(41\) | 58841.0i | 0.853745i | 0.904312 | + | 0.426873i | \(0.140385\pi\) | ||||
−0.904312 | + | 0.426873i | \(0.859615\pi\) | |||||||
\(42\) | 6680.72 | + | 19622.4i | 0.0901727 | + | 0.264853i | ||||
\(43\) | −135972. | −1.71019 | −0.855097 | − | 0.518468i | \(-0.826503\pi\) | ||||
−0.855097 | + | 0.518468i | \(0.826503\pi\) | |||||||
\(44\) | 50985.2i | 0.598531i | ||||||||
\(45\) | −64294.8 | − | 83477.4i | −0.705567 | − | 0.916076i | ||||
\(46\) | −91082.1 | −0.935750 | ||||||||
\(47\) | 28061.3i | 0.270280i | 0.990826 | + | 0.135140i | \(0.0431485\pi\) | ||||
−0.990826 | + | 0.135140i | \(0.956852\pi\) | |||||||
\(48\) | −35971.0 | + | 12246.8i | −0.325259 | + | 0.110739i | ||||
\(49\) | 16807.0 | 0.142857 | ||||||||
\(50\) | − | 31184.2i | − | 0.249474i | ||||||
\(51\) | −52431.2 | − | 153999.i | −0.395257 | − | 1.16094i | ||||
\(52\) | −36422.6 | −0.259036 | ||||||||
\(53\) | − | 125789.i | − | 0.844921i | −0.906381 | − | 0.422460i | \(-0.861167\pi\) | ||
0.906381 | − | 0.422460i | \(-0.138833\pi\) | |||||||
\(54\) | 97091.7 | + | 64494.0i | 0.616596 | + | 0.409579i | ||||
\(55\) | 254714. | 1.53096 | ||||||||
\(56\) | 71345.5i | 0.406259i | ||||||||
\(57\) | −239612. | + | 81579.4i | −1.29385 | + | 0.440510i | ||||
\(58\) | 101031. | 0.517808 | ||||||||
\(59\) | 181093.i | 0.881751i | 0.897568 | + | 0.440876i | \(0.145332\pi\) | ||||
−0.897568 | + | 0.440876i | \(0.854668\pi\) | |||||||
\(60\) | −36388.9 | − | 106880.i | −0.168467 | − | 0.494816i | ||||
\(61\) | 300687. | 1.32472 | 0.662362 | − | 0.749184i | \(-0.269554\pi\) | ||||
0.662362 | + | 0.749184i | \(0.269554\pi\) | |||||||
\(62\) | − | 121427.i | − | 0.509497i | ||||||
\(63\) | 74874.7 | − | 57669.0i | 0.299442 | − | 0.230633i | ||||
\(64\) | −249291. | −0.950970 | ||||||||
\(65\) | 181961.i | 0.662582i | ||||||||
\(66\) | −266736. | + | 90813.8i | −0.927789 | + | 0.315878i | ||||
\(67\) | 314063. | 1.04422 | 0.522111 | − | 0.852877i | \(-0.325145\pi\) | ||||
0.522111 | + | 0.852877i | \(0.325145\pi\) | |||||||
\(68\) | − | 174318.i | − | 0.554389i | ||||||
\(69\) | 133842. | + | 393118.i | 0.407424 | + | 1.19667i | ||||
\(70\) | 110964. | 0.323511 | ||||||||
\(71\) | − | 438176.i | − | 1.22426i | −0.790758 | − | 0.612129i | \(-0.790313\pi\) | ||
0.790758 | − | 0.612129i | \(-0.209687\pi\) | |||||||
\(72\) | 244804. | + | 317842.i | 0.655875 | + | 0.851558i | ||||
\(73\) | 49885.6 | 0.128235 | 0.0641175 | − | 0.997942i | \(-0.479577\pi\) | ||||
0.0641175 | + | 0.997942i | \(0.479577\pi\) | |||||||
\(74\) | 50149.7i | 0.123758i | ||||||||
\(75\) | −134593. | + | 45824.2i | −0.319036 | + | 0.108620i | ||||
\(76\) | −271226. | −0.617861 | ||||||||
\(77\) | 228465.i | 0.500434i | ||||||||
\(78\) | −64875.1 | − | 190549.i | −0.136708 | − | 0.401535i | ||||
\(79\) | 505643. | 1.02556 | 0.512782 | − | 0.858519i | \(-0.328615\pi\) | ||||
0.512782 | + | 0.858519i | \(0.328615\pi\) | |||||||
\(80\) | 203415.i | 0.397295i | ||||||||
\(81\) | 135688. | − | 513827.i | 0.255321 | − | 0.966856i | ||||
\(82\) | −348449. | −0.631971 | ||||||||
\(83\) | 341518.i | 0.597281i | 0.954366 | + | 0.298641i | \(0.0965332\pi\) | ||||
−0.954366 | + | 0.298641i | \(0.903467\pi\) | |||||||
\(84\) | 95865.8 | − | 32638.8i | 0.161743 | − | 0.0550677i | ||||
\(85\) | −870863. | −1.41806 | ||||||||
\(86\) | − | 805211.i | − | 1.26594i | ||||||
\(87\) | −148461. | − | 436056.i | −0.225453 | − | 0.662192i | ||||
\(88\) | −969830. | −1.42314 | ||||||||
\(89\) | − | 824180.i | − | 1.16910i | −0.811357 | − | 0.584550i | \(-0.801271\pi\) | ||
0.811357 | − | 0.584550i | \(-0.198729\pi\) | |||||||
\(90\) | 494342. | − | 380746.i | 0.678110 | − | 0.522285i | ||||
\(91\) | −163210. | −0.216582 | ||||||||
\(92\) | 444984.i | 0.571454i | ||||||||
\(93\) | −524090. | + | 178434.i | −0.651564 | + | 0.221834i | ||||
\(94\) | −166175. | −0.200071 | ||||||||
\(95\) | 1.35500e6i | 1.58041i | ||||||||
\(96\) | 233969. | + | 687207.i | 0.264451 | + | 0.776736i | ||||
\(97\) | −142772. | −0.156433 | −0.0782167 | − | 0.996936i | \(-0.524923\pi\) | ||||
−0.0782167 | + | 0.996936i | \(0.524923\pi\) | |||||||
\(98\) | 99528.9i | 0.105748i | ||||||||
\(99\) | 783919. | + | 1.01780e6i | 0.807915 | + | 1.04896i | ||||
\(100\) | −152351. | −0.152351 | ||||||||
\(101\) | − | 656702.i | − | 0.637388i | −0.947858 | − | 0.318694i | \(-0.896756\pi\) | ||
0.947858 | − | 0.318694i | \(-0.103244\pi\) | |||||||
\(102\) | 911965. | − | 310491.i | 0.859365 | − | 0.292583i | ||||
\(103\) | 773197. | 0.707585 | 0.353792 | − | 0.935324i | \(-0.384892\pi\) | ||||
0.353792 | + | 0.935324i | \(0.384892\pi\) | |||||||
\(104\) | − | 692823.i | − | 0.615917i | ||||||
\(105\) | −163058. | − | 478930.i | −0.140856 | − | 0.413718i | ||||
\(106\) | 744908. | 0.625439 | ||||||||
\(107\) | 1.45353e6i | 1.18651i | 0.805014 | + | 0.593256i | \(0.202158\pi\) | ||||
−0.805014 | + | 0.593256i | \(0.797842\pi\) | |||||||
\(108\) | 315087. | − | 474344.i | 0.250126 | − | 0.376550i | ||||
\(109\) | −439044. | −0.339022 | −0.169511 | − | 0.985528i | \(-0.554219\pi\) | ||||
−0.169511 | + | 0.985528i | \(0.554219\pi\) | |||||||
\(110\) | 1.50838e6i | 1.13327i | ||||||||
\(111\) | 216450. | − | 73693.4i | 0.158266 | − | 0.0538840i | ||||
\(112\) | −182452. | −0.129866 | ||||||||
\(113\) | − | 1.30626e6i | − | 0.905307i | −0.891686 | − | 0.452653i | \(-0.850477\pi\) | ||
0.891686 | − | 0.452653i | \(-0.149523\pi\) | |||||||
\(114\) | −483102. | − | 1.41895e6i | −0.326080 | − | 0.957753i | ||||
\(115\) | 2.22307e6 | 1.46171 | ||||||||
\(116\) | − | 493588.i | − | 0.316221i | ||||||
\(117\) | −727094. | + | 560012.i | −0.453976 | + | 0.349655i | ||||
\(118\) | −1.07241e6 | −0.652702 | ||||||||
\(119\) | − | 781117.i | − | 0.463527i | ||||||
\(120\) | 2.03305e6 | − | 692181.i | 1.17654 | − | 0.400568i | ||||
\(121\) | −1.33406e6 | −0.753040 | ||||||||
\(122\) | 1.78063e6i | 0.980606i | ||||||||
\(123\) | 512034. | + | 1.50393e6i | 0.275159 | + | 0.808188i | ||||
\(124\) | −593237. | −0.311145 | ||||||||
\(125\) | − | 1.49727e6i | − | 0.766601i | ||||||
\(126\) | 341508. | + | 443398.i | 0.170722 | + | 0.221657i | ||||
\(127\) | 2.38957e6 | 1.16656 | 0.583281 | − | 0.812270i | \(-0.301768\pi\) | ||||
0.583281 | + | 0.812270i | \(0.301768\pi\) | |||||||
\(128\) | 244487.i | 0.116580i | ||||||||
\(129\) | −3.47535e6 | + | 1.18323e6i | −1.61894 | + | 0.551189i | ||||
\(130\) | −1.07755e6 | −0.490465 | ||||||||
\(131\) | − | 2.11936e6i | − | 0.942739i | −0.881936 | − | 0.471370i | \(-0.843760\pi\) | ||
0.881936 | − | 0.471370i | \(-0.156240\pi\) | |||||||
\(132\) | 443673. | + | 1.30314e6i | 0.192904 | + | 0.566592i | ||||
\(133\) | −1.21536e6 | −0.516597 | ||||||||
\(134\) | 1.85984e6i | 0.772969i | ||||||||
\(135\) | −2.36975e6 | − | 1.57413e6i | −0.963165 | − | 0.639791i | ||||
\(136\) | 3.31583e6 | 1.31818 | ||||||||
\(137\) | − | 1.08490e6i | − | 0.421919i | −0.977495 | − | 0.210959i | \(-0.932341\pi\) | ||
0.977495 | − | 0.210959i | \(-0.0676588\pi\) | |||||||
\(138\) | −2.32799e6 | + | 792597.i | −0.885817 | + | 0.301589i | ||||
\(139\) | −3.92436e6 | −1.46125 | −0.730626 | − | 0.682778i | \(-0.760771\pi\) | ||||
−0.730626 | + | 0.682778i | \(0.760771\pi\) | |||||||
\(140\) | − | 542119.i | − | 0.197565i | ||||||
\(141\) | 244190. | + | 717226.i | 0.0871103 | + | 0.255858i | ||||
\(142\) | 2.59482e6 | 0.906237 | ||||||||
\(143\) | − | 2.21858e6i | − | 0.758693i | ||||||
\(144\) | −812820. | + | 626039.i | −0.272212 | + | 0.209659i | ||||
\(145\) | −2.46589e6 | −0.808852 | ||||||||
\(146\) | 295416.i | 0.0949238i | ||||||||
\(147\) | 429574. | − | 146254.i | 0.135234 | − | 0.0460423i | ||||
\(148\) | 245008. | 0.0755779 | ||||||||
\(149\) | 2.16645e6i | 0.654922i | 0.944865 | + | 0.327461i | \(0.106193\pi\) | ||||
−0.944865 | + | 0.327461i | \(0.893807\pi\) | |||||||
\(150\) | −271365. | − | 797045.i | −0.0804044 | − | 0.236161i | ||||
\(151\) | 4.33862e6 | 1.26015 | 0.630073 | − | 0.776536i | \(-0.283025\pi\) | ||||
0.630073 | + | 0.776536i | \(0.283025\pi\) | |||||||
\(152\) | − | 5.15921e6i | − | 1.46910i | ||||||
\(153\) | −2.68021e6 | − | 3.47985e6i | −0.748331 | − | 0.971598i | ||||
\(154\) | −1.35294e6 | −0.370438 | ||||||||
\(155\) | 2.96372e6i | 0.795869i | ||||||||
\(156\) | −930934. | + | 316949.i | −0.245214 | + | 0.0834865i | ||||
\(157\) | 5.30473e6 | 1.37077 | 0.685384 | − | 0.728182i | \(-0.259634\pi\) | ||||
0.685384 | + | 0.728182i | \(0.259634\pi\) | |||||||
\(158\) | 2.99435e6i | 0.759157i | ||||||||
\(159\) | −1.09462e6 | − | 3.21508e6i | −0.272315 | − | 0.799835i | ||||
\(160\) | 3.88614e6 | 0.948764 | ||||||||
\(161\) | 1.99397e6i | 0.477795i | ||||||||
\(162\) | 3.04282e6 | + | 803527.i | 0.715700 | + | 0.188997i | ||||
\(163\) | 4.58667e6 | 1.05910 | 0.529548 | − | 0.848280i | \(-0.322362\pi\) | ||||
0.529548 | + | 0.848280i | \(0.322362\pi\) | |||||||
\(164\) | 1.70236e6i | 0.385939i | ||||||||
\(165\) | 6.51030e6 | − | 2.21652e6i | 1.44927 | − | 0.493424i | ||||
\(166\) | −2.02242e6 | −0.442128 | ||||||||
\(167\) | 6.23982e6i | 1.33975i | 0.742476 | + | 0.669873i | \(0.233651\pi\) | ||||
−0.742476 | + | 0.669873i | \(0.766349\pi\) | |||||||
\(168\) | 620849. | + | 1.82354e6i | 0.130936 | + | 0.384580i | ||||
\(169\) | −3.24191e6 | −0.671647 | ||||||||
\(170\) | − | 5.15714e6i | − | 1.04969i | ||||||
\(171\) | −5.41441e6 | + | 4.17021e6i | −1.08284 | + | 0.834008i | ||||
\(172\) | −3.93388e6 | −0.773100 | ||||||||
\(173\) | 8.17326e6i | 1.57854i | 0.614043 | + | 0.789272i | \(0.289542\pi\) | ||||
−0.614043 | + | 0.789272i | \(0.710458\pi\) | |||||||
\(174\) | 2.58227e6 | − | 879168.i | 0.490177 | − | 0.166888i | ||||
\(175\) | −682686. | −0.127382 | ||||||||
\(176\) | − | 2.48015e6i | − | 0.454926i | ||||||
\(177\) | 1.57587e6 | + | 4.62861e6i | 0.284185 | + | 0.834700i | ||||
\(178\) | 4.88069e6 | 0.865408 | ||||||||
\(179\) | − | 7.10092e6i | − | 1.23810i | −0.785352 | − | 0.619050i | \(-0.787518\pi\) | ||
0.785352 | − | 0.619050i | \(-0.212482\pi\) | |||||||
\(180\) | −1.86014e6 | − | 2.41512e6i | −0.318955 | − | 0.414116i | ||||
\(181\) | −6.92233e6 | −1.16739 | −0.583696 | − | 0.811972i | \(-0.698394\pi\) | ||||
−0.583696 | + | 0.811972i | \(0.698394\pi\) | |||||||
\(182\) | − | 966506.i | − | 0.160321i | ||||||
\(183\) | 7.68534e6 | − | 2.61658e6i | 1.25404 | − | 0.426954i | ||||
\(184\) | −8.46440e6 | −1.35876 | ||||||||
\(185\) | − | 1.22402e6i | − | 0.193319i | ||||||
\(186\) | −1.05666e6 | − | 3.10359e6i | −0.164209 | − | 0.482310i | ||||
\(187\) | 1.06181e7 | 1.62375 | ||||||||
\(188\) | 811855.i | 0.122181i | ||||||||
\(189\) | 1.41191e6 | − | 2.12554e6i | 0.209132 | − | 0.314835i | ||||
\(190\) | −8.02415e6 | −1.16987 | ||||||||
\(191\) | − | 5.17663e6i | − | 0.742929i | −0.928447 | − | 0.371464i | \(-0.878856\pi\) | ||
0.928447 | − | 0.371464i | \(-0.121144\pi\) | |||||||
\(192\) | −6.37169e6 | + | 2.16933e6i | −0.900225 | + | 0.306494i | ||||
\(193\) | −7.99433e6 | −1.11201 | −0.556007 | − | 0.831178i | \(-0.687667\pi\) | ||||
−0.556007 | + | 0.831178i | \(0.687667\pi\) | |||||||
\(194\) | − | 845480.i | − | 0.115797i | ||||||
\(195\) | 1.58343e6 | + | 4.65080e6i | 0.213548 | + | 0.627225i | ||||
\(196\) | 486251. | 0.0645792 | ||||||||
\(197\) | 3.39988e6i | 0.444698i | 0.974967 | + | 0.222349i | \(0.0713724\pi\) | ||||
−0.974967 | + | 0.222349i | \(0.928628\pi\) | |||||||
\(198\) | −6.02730e6 | + | 4.64227e6i | −0.776474 | + | 0.598046i | ||||
\(199\) | −7.26597e6 | −0.922007 | −0.461004 | − | 0.887398i | \(-0.652510\pi\) | ||||
−0.461004 | + | 0.887398i | \(0.652510\pi\) | |||||||
\(200\) | − | 2.89799e6i | − | 0.362249i | ||||||
\(201\) | 8.02723e6 | − | 2.73298e6i | 0.988501 | − | 0.336549i | ||||
\(202\) | 3.88890e6 | 0.471816 | ||||||||
\(203\) | − | 2.21177e6i | − | 0.264394i | ||||||
\(204\) | −1.51691e6 | − | 4.45543e6i | −0.178678 | − | 0.524806i | ||||
\(205\) | 8.50470e6 | 0.987182 | ||||||||
\(206\) | 4.57877e6i | 0.523778i | ||||||||
\(207\) | 6.84182e6 | + | 8.88309e6i | 0.771366 | + | 1.00151i | ||||
\(208\) | 1.77176e6 | 0.196886 | ||||||||
\(209\) | − | 1.65210e7i | − | 1.80966i | ||||||
\(210\) | 2.83616e6 | − | 965610.i | 0.306248 | − | 0.104266i | ||||
\(211\) | −1.75679e7 | −1.87013 | −0.935067 | − | 0.354471i | \(-0.884661\pi\) | ||||
−0.935067 | + | 0.354471i | \(0.884661\pi\) | |||||||
\(212\) | − | 3.63927e6i | − | 0.381950i | ||||||
\(213\) | −3.81300e6 | − | 1.11994e7i | −0.394574 | − | 1.15893i | ||||
\(214\) | −8.60760e6 | −0.878296 | ||||||||
\(215\) | 1.96530e7i | 1.97749i | ||||||||
\(216\) | 9.02287e6 | + | 5.99352e6i | 0.895331 | + | 0.594731i | ||||
\(217\) | −2.65829e6 | −0.260150 | ||||||||
\(218\) | − | 2.59996e6i | − | 0.250956i | ||||||
\(219\) | 1.27504e6 | − | 434104.i | 0.121392 | − | 0.0413296i | ||||
\(220\) | 7.36925e6 | 0.692078 | ||||||||
\(221\) | 7.58528e6i | 0.702740i | ||||||||
\(222\) | 436403. | + | 1.28179e6i | 0.0398868 | + | 0.117154i | ||||
\(223\) | 2.19380e6 | 0.197825 | 0.0989127 | − | 0.995096i | \(-0.468464\pi\) | ||||
0.0989127 | + | 0.995096i | \(0.468464\pi\) | |||||||
\(224\) | 3.48565e6i | 0.310127i | ||||||||
\(225\) | −3.04134e6 | + | 2.34246e6i | −0.267004 | + | 0.205648i | ||||
\(226\) | 7.73553e6 | 0.670139 | ||||||||
\(227\) | − | 1.20937e7i | − | 1.03391i | −0.856014 | − | 0.516953i | \(-0.827066\pi\) | ||
0.856014 | − | 0.516953i | \(-0.172934\pi\) | |||||||
\(228\) | −6.93234e6 | + | 2.36021e6i | −0.584891 | + | 0.199134i | ||||
\(229\) | 4.36562e6 | 0.363529 | 0.181765 | − | 0.983342i | \(-0.441819\pi\) | ||||
0.181765 | + | 0.983342i | \(0.441819\pi\) | |||||||
\(230\) | 1.31647e7i | 1.08200i | ||||||||
\(231\) | 1.98810e6 | + | 5.83939e6i | 0.161288 | + | 0.473730i | ||||
\(232\) | 9.38892e6 | 0.751885 | ||||||||
\(233\) | 6.97793e6i | 0.551644i | 0.961209 | + | 0.275822i | \(0.0889501\pi\) | ||||
−0.961209 | + | 0.275822i | \(0.911050\pi\) | |||||||
\(234\) | −3.31632e6 | − | 4.30575e6i | −0.258827 | − | 0.336048i | ||||
\(235\) | 4.05590e6 | 0.312524 | ||||||||
\(236\) | 5.23929e6i | 0.398599i | ||||||||
\(237\) | 1.29239e7 | − | 4.40010e6i | 0.970838 | − | 0.330535i | ||||
\(238\) | 4.62567e6 | 0.343118 | ||||||||
\(239\) | − | 1.31069e7i | − | 0.960075i | −0.877248 | − | 0.480038i | \(-0.840623\pi\) | ||
0.877248 | − | 0.480038i | \(-0.159377\pi\) | |||||||
\(240\) | 1.77012e6 | + | 5.19914e6i | 0.128047 | + | 0.376095i | ||||
\(241\) | 5.41621e6 | 0.386941 | 0.193470 | − | 0.981106i | \(-0.438026\pi\) | ||||
0.193470 | + | 0.981106i | \(0.438026\pi\) | |||||||
\(242\) | − | 7.90011e6i | − | 0.557426i | ||||||
\(243\) | −1.00324e6 | − | 1.43138e7i | −0.0699175 | − | 0.997553i | ||||
\(244\) | 8.69932e6 | 0.598847 | ||||||||
\(245\) | − | 2.42923e6i | − | 0.165185i | ||||||
\(246\) | −8.90608e6 | + | 3.03220e6i | −0.598248 | + | 0.203682i | ||||
\(247\) | 1.18022e7 | 0.783197 | ||||||||
\(248\) | − | 1.12844e7i | − | 0.739817i | ||||||
\(249\) | 2.97189e6 | + | 8.72893e6i | 0.192501 | + | 0.565410i | ||||
\(250\) | 8.86662e6 | 0.567464 | ||||||||
\(251\) | 2.92888e6i | 0.185217i | 0.995703 | + | 0.0926083i | \(0.0295204\pi\) | ||||
−0.995703 | + | 0.0926083i | \(0.970480\pi\) | |||||||
\(252\) | 2.16623e6 | − | 1.66845e6i | 0.135364 | − | 0.104258i | ||||
\(253\) | −2.71049e7 | −1.67374 | ||||||||
\(254\) | 1.41507e7i | 0.863529i | ||||||||
\(255\) | −2.22586e7 | + | 7.57825e6i | −1.34239 | + | 0.457034i | ||||
\(256\) | −1.74024e7 | −1.03727 | ||||||||
\(257\) | − | 1.16323e7i | − | 0.685280i | −0.939467 | − | 0.342640i | \(-0.888679\pi\) | ||
0.939467 | − | 0.342640i | \(-0.111321\pi\) | |||||||
\(258\) | −7.00694e6 | − | 2.05806e7i | −0.408009 | − | 1.19839i | ||||
\(259\) | 1.09788e6 | 0.0631911 | ||||||||
\(260\) | 5.26441e6i | 0.299523i | ||||||||
\(261\) | −7.58911e6 | − | 9.85335e6i | −0.426844 | − | 0.554195i | ||||
\(262\) | 1.25506e7 | 0.697847 | ||||||||
\(263\) | 2.06892e7i | 1.13730i | 0.822578 | + | 0.568652i | \(0.192535\pi\) | ||||
−0.822578 | + | 0.568652i | \(0.807465\pi\) | |||||||
\(264\) | −2.47881e7 | + | 8.43946e6i | −1.34720 | + | 0.458673i | ||||
\(265\) | −1.81812e7 | −0.976978 | ||||||||
\(266\) | − | 7.19723e6i | − | 0.382402i | ||||||
\(267\) | −7.17201e6 | − | 2.10654e7i | −0.376797 | − | 1.10672i | ||||
\(268\) | 9.08631e6 | 0.472045 | ||||||||
\(269\) | 2.91650e7i | 1.49832i | 0.662388 | + | 0.749161i | \(0.269543\pi\) | ||||
−0.662388 | + | 0.749161i | \(0.730457\pi\) | |||||||
\(270\) | 9.32177e6 | − | 1.40333e7i | 0.473595 | − | 0.712967i | ||||
\(271\) | −7.38727e6 | −0.371173 | −0.185586 | − | 0.982628i | \(-0.559418\pi\) | ||||
−0.185586 | + | 0.982628i | \(0.559418\pi\) | |||||||
\(272\) | 8.47960e6i | 0.421375i | ||||||||
\(273\) | −4.17151e6 | + | 1.42025e6i | −0.205024 | + | 0.0698034i | ||||
\(274\) | 6.42465e6 | 0.312318 | ||||||||
\(275\) | − | 9.28004e6i | − | 0.446223i | ||||||
\(276\) | 3.87225e6 | + | 1.13735e7i | 0.184177 | + | 0.540961i | ||||
\(277\) | 2.79150e7 | 1.31340 | 0.656702 | − | 0.754150i | \(-0.271951\pi\) | ||||
0.656702 | + | 0.754150i | \(0.271951\pi\) | |||||||
\(278\) | − | 2.32396e7i | − | 1.08167i | ||||||
\(279\) | −1.18426e7 | + | 9.12126e6i | −0.545300 | + | 0.419993i | ||||
\(280\) | 1.03121e7 | 0.469755 | ||||||||
\(281\) | − | 9.14595e6i | − | 0.412202i | −0.978531 | − | 0.206101i | \(-0.933922\pi\) | ||
0.978531 | − | 0.206101i | \(-0.0660775\pi\) | |||||||
\(282\) | −4.24732e6 | + | 1.44606e6i | −0.189395 | + | 0.0644820i | ||||
\(283\) | −2.54163e7 | −1.12138 | −0.560690 | − | 0.828026i | \(-0.689464\pi\) | ||||
−0.560690 | + | 0.828026i | \(0.689464\pi\) | |||||||
\(284\) | − | 1.26771e7i | − | 0.553431i | ||||||
\(285\) | 1.17912e7 | + | 3.46329e7i | 0.509360 | + | 1.49608i | ||||
\(286\) | 1.31381e7 | 0.561610 | ||||||||
\(287\) | 7.62825e6i | 0.322685i | ||||||||
\(288\) | 1.19601e7 | + | 1.55285e7i | 0.500678 | + | 0.650057i | ||||
\(289\) | −1.21654e7 | −0.504003 | ||||||||
\(290\) | − | 1.46027e7i | − | 0.598739i | ||||||
\(291\) | −3.64916e6 | + | 1.24241e6i | −0.148086 | + | 0.0504179i | ||||
\(292\) | 1.44326e6 | 0.0579691 | ||||||||
\(293\) | − | 1.38751e7i | − | 0.551611i | −0.961213 | − | 0.275806i | \(-0.911055\pi\) | ||
0.961213 | − | 0.275806i | \(-0.0889446\pi\) | |||||||
\(294\) | 866100. | + | 2.54388e6i | 0.0340821 | + | 0.100105i | ||||
\(295\) | 2.61747e7 | 1.01957 | ||||||||
\(296\) | 4.66049e6i | 0.179703i | ||||||||
\(297\) | 2.88933e7 | + | 1.91926e7i | 1.10288 | + | 0.732597i | ||||
\(298\) | −1.28294e7 | −0.484796 | ||||||||
\(299\) | − | 1.93631e7i | − | 0.724371i | ||||||
\(300\) | −3.89398e6 | + | 1.32576e6i | −0.144222 | + | 0.0491022i | ||||
\(301\) | −1.76277e7 | −0.646393 | ||||||||
\(302\) | 2.56927e7i | 0.932802i | ||||||||
\(303\) | −5.71462e6 | − | 1.67848e7i | −0.205428 | − | 0.603377i | ||||
\(304\) | 1.31937e7 | 0.469618 | ||||||||
\(305\) | − | 4.34604e7i | − | 1.53177i | ||||||
\(306\) | 2.06072e7 | − | 1.58718e7i | 0.719210 | − | 0.553940i | ||||
\(307\) | −2.13868e6 | −0.0739147 | −0.0369573 | − | 0.999317i | \(-0.511767\pi\) | ||||
−0.0369573 | + | 0.999317i | \(0.511767\pi\) | |||||||
\(308\) | 6.60982e6i | 0.226223i | ||||||||
\(309\) | 1.97623e7 | − | 6.72836e6i | 0.669827 | − | 0.228052i | ||||
\(310\) | −1.75508e7 | −0.589129 | ||||||||
\(311\) | − | 2.20443e7i | − | 0.732851i | −0.930447 | − | 0.366426i | \(-0.880581\pi\) | ||
0.930447 | − | 0.366426i | \(-0.119419\pi\) | |||||||
\(312\) | −6.02894e6 | − | 1.77080e7i | −0.198508 | − | 0.583051i | ||||
\(313\) | 7.52711e6 | 0.245468 | 0.122734 | − | 0.992440i | \(-0.460834\pi\) | ||||
0.122734 | + | 0.992440i | \(0.460834\pi\) | |||||||
\(314\) | 3.14139e7i | 1.01469i | ||||||||
\(315\) | −8.33530e6 | − | 1.08222e7i | −0.266679 | − | 0.346244i | ||||
\(316\) | 1.46290e7 | 0.463610 | ||||||||
\(317\) | 1.10809e7i | 0.347855i | 0.984758 | + | 0.173928i | \(0.0556459\pi\) | ||||
−0.984758 | + | 0.173928i | \(0.944354\pi\) | |||||||
\(318\) | 1.90393e7 | − | 6.48219e6i | 0.592065 | − | 0.201577i | ||||
\(319\) | 3.00655e7 | 0.926181 | ||||||||
\(320\) | 3.60318e7i | 1.09960i | ||||||||
\(321\) | 1.26486e7 | + | 3.71511e7i | 0.382408 | + | 1.12320i | ||||
\(322\) | −1.18081e7 | −0.353680 | ||||||||
\(323\) | 5.64849e7i | 1.67620i | ||||||||
\(324\) | 3.92565e6 | − | 1.48658e7i | 0.115419 | − | 0.437071i | ||||
\(325\) | 6.62943e6 | 0.193119 | ||||||||
\(326\) | 2.71617e7i | 0.783978i | ||||||||
\(327\) | −1.12216e7 | + | 3.82056e6i | −0.320932 | + | 0.109266i | ||||
\(328\) | −3.23818e7 | −0.917656 | ||||||||
\(329\) | 3.63792e6i | 0.102156i | ||||||||
\(330\) | 1.31260e7 | + | 3.85532e7i | 0.365249 | + | 1.07280i | ||||
\(331\) | −3.15332e7 | −0.869528 | −0.434764 | − | 0.900544i | \(-0.643168\pi\) | ||||
−0.434764 | + | 0.900544i | \(0.643168\pi\) | |||||||
\(332\) | 9.88060e6i | 0.270003i | ||||||||
\(333\) | 4.89102e6 | − | 3.76710e6i | 0.132455 | − | 0.102017i | ||||
\(334\) | −3.69514e7 | −0.991725 | ||||||||
\(335\) | − | 4.53938e7i | − | 1.20743i | ||||||
\(336\) | −4.66334e6 | + | 1.58770e6i | −0.122936 | + | 0.0418553i | ||||
\(337\) | 3.43359e7 | 0.897137 | 0.448568 | − | 0.893748i | \(-0.351934\pi\) | ||||
0.448568 | + | 0.893748i | \(0.351934\pi\) | |||||||
\(338\) | − | 1.91982e7i | − | 0.497176i | ||||||
\(339\) | −1.13671e7 | − | 3.33871e7i | −0.291777 | − | 0.856999i | ||||
\(340\) | −2.51953e7 | −0.641038 | ||||||||
\(341\) | − | 3.61353e7i | − | 0.911316i | ||||||
\(342\) | −2.46955e7 | − | 3.20634e7i | −0.617361 | − | 0.801552i | ||||
\(343\) | 2.17889e6 | 0.0539949 | ||||||||
\(344\) | − | 7.48294e7i | − | 1.83822i | ||||||
\(345\) | 5.68200e7 | − | 1.93452e7i | 1.38371 | − | 0.471102i | ||||
\(346\) | −4.84010e7 | −1.16849 | ||||||||
\(347\) | 5.43933e7i | 1.30184i | 0.759147 | + | 0.650919i | \(0.225616\pi\) | ||||
−0.759147 | + | 0.650919i | \(0.774384\pi\) | |||||||
\(348\) | −4.29520e6 | − | 1.26157e7i | −0.101917 | − | 0.299347i | ||||
\(349\) | −9.96472e6 | −0.234417 | −0.117208 | − | 0.993107i | \(-0.537395\pi\) | ||||
−0.117208 | + | 0.993107i | \(0.537395\pi\) | |||||||
\(350\) | − | 4.04278e6i | − | 0.0942921i | ||||||
\(351\) | −1.37107e7 | + | 2.06407e7i | −0.317059 | + | 0.477312i | ||||
\(352\) | −4.73820e7 | −1.08639 | ||||||||
\(353\) | 7.31427e7i | 1.66283i | 0.555656 | + | 0.831413i | \(0.312467\pi\) | ||||
−0.555656 | + | 0.831413i | \(0.687533\pi\) | |||||||
\(354\) | −2.74100e7 | + | 9.33211e6i | −0.617873 | + | 0.210363i | ||||
\(355\) | −6.33326e7 | −1.41560 | ||||||||
\(356\) | − | 2.38447e7i | − | 0.528497i | ||||||
\(357\) | −6.79728e6 | − | 1.99648e7i | −0.149393 | − | 0.438793i | ||||
\(358\) | 4.20507e7 | 0.916483 | ||||||||
\(359\) | − | 1.99515e7i | − | 0.431213i | −0.976480 | − | 0.215607i | \(-0.930827\pi\) | ||
0.976480 | − | 0.215607i | \(-0.0691729\pi\) | |||||||
\(360\) | 4.59399e7 | − | 3.53832e7i | 0.984652 | − | 0.758386i | ||||
\(361\) | 4.08407e7 | 0.868104 | ||||||||
\(362\) | − | 4.09932e7i | − | 0.864143i | ||||||
\(363\) | −3.40975e7 | + | 1.16090e7i | −0.712857 | + | 0.242702i | ||||
\(364\) | −4.72189e6 | −0.0979066 | ||||||||
\(365\) | − | 7.21031e6i | − | 0.148277i | ||||||
\(366\) | 1.54950e7 | + | 4.55116e7i | 0.316046 | + | 0.928279i | ||||
\(367\) | 1.97764e6 | 0.0400082 | 0.0200041 | − | 0.999800i | \(-0.493632\pi\) | ||||
0.0200041 | + | 0.999800i | \(0.493632\pi\) | |||||||
\(368\) | − | 2.16461e7i | − | 0.434345i | ||||||
\(369\) | 2.61744e7 | + | 3.39836e7i | 0.520952 | + | 0.676380i | ||||
\(370\) | 7.24849e6 | 0.143101 | ||||||||
\(371\) | − | 1.63076e7i | − | 0.319350i | ||||||
\(372\) | −1.51627e7 | + | 5.16235e6i | −0.294542 | + | 0.100281i | ||||
\(373\) | 2.62130e7 | 0.505114 | 0.252557 | − | 0.967582i | \(-0.418728\pi\) | ||||
0.252557 | + | 0.967582i | \(0.418728\pi\) | |||||||
\(374\) | 6.28787e7i | 1.20196i | ||||||||
\(375\) | −1.30292e7 | − | 3.82690e7i | −0.247073 | − | 0.725694i | ||||
\(376\) | −1.54429e7 | −0.290513 | ||||||||
\(377\) | 2.14780e7i | 0.400839i | ||||||||
\(378\) | 1.25871e7 | + | 8.36112e6i | 0.233051 | + | 0.154806i | ||||
\(379\) | 5.21829e7 | 0.958540 | 0.479270 | − | 0.877668i | \(-0.340901\pi\) | ||||
0.479270 | + | 0.877668i | \(0.340901\pi\) | |||||||
\(380\) | 3.92022e7i | 0.714430i | ||||||||
\(381\) | 6.10756e7 | − | 2.07940e7i | 1.10431 | − | 0.375979i | ||||
\(382\) | 3.06553e7 | 0.549941 | ||||||||
\(383\) | 4.08689e7i | 0.727439i | 0.931509 | + | 0.363719i | \(0.118493\pi\) | ||||
−0.931509 | + | 0.363719i | \(0.881507\pi\) | |||||||
\(384\) | 2.12752e6 | + | 6.24890e6i | 0.0375734 | + | 0.110359i | ||||
\(385\) | 3.30216e7 | 0.578650 | ||||||||
\(386\) | − | 4.73414e7i | − | 0.823150i | ||||||
\(387\) | −7.85309e7 | + | 6.04850e7i | −1.35490 | + | 1.04355i | ||||
\(388\) | −4.13062e6 | −0.0707163 | ||||||||
\(389\) | 6.03432e7i | 1.02513i | 0.858648 | + | 0.512566i | \(0.171305\pi\) | ||||
−0.858648 | + | 0.512566i | \(0.828695\pi\) | |||||||
\(390\) | −2.75414e7 | + | 9.37686e6i | −0.464293 | + | 0.158075i | ||||
\(391\) | 9.26713e7 | 1.55030 | ||||||||
\(392\) | 9.24936e6i | 0.153551i | ||||||||
\(393\) | −1.84427e7 | − | 5.41693e7i | −0.303841 | − | 0.892434i | ||||
\(394\) | −2.01337e7 | −0.329180 | ||||||||
\(395\) | − | 7.30841e7i | − | 1.18586i | ||||||
\(396\) | 2.26799e7 | + | 2.94465e7i | 0.365221 | + | 0.474186i | ||||
\(397\) | −2.28136e7 | −0.364604 | −0.182302 | − | 0.983243i | \(-0.558355\pi\) | ||||
−0.182302 | + | 0.983243i | \(0.558355\pi\) | |||||||
\(398\) | − | 4.30281e7i | − | 0.682501i | ||||||
\(399\) | −3.10638e7 | + | 1.05761e7i | −0.489030 | + | 0.166497i | ||||
\(400\) | 7.41106e6 | 0.115798 | ||||||||
\(401\) | 1.73802e7i | 0.269538i | 0.990877 | + | 0.134769i | \(0.0430293\pi\) | ||||
−0.990877 | + | 0.134769i | \(0.956971\pi\) | |||||||
\(402\) | 1.61843e7 | + | 4.75362e7i | 0.249125 | + | 0.731722i | ||||
\(403\) | 2.58142e7 | 0.394406 | ||||||||
\(404\) | − | 1.89993e7i | − | 0.288134i | ||||||
\(405\) | −7.42670e7 | − | 1.96119e7i | −1.11797 | − | 0.295227i | ||||
\(406\) | 1.30978e7 | 0.195713 | ||||||||
\(407\) | 1.49240e7i | 0.221361i | ||||||||
\(408\) | 8.47502e7 | − | 2.88544e7i | 1.24784 | − | 0.424846i | ||||
\(409\) | 3.55479e6 | 0.0519570 | 0.0259785 | − | 0.999663i | \(-0.491730\pi\) | ||||
0.0259785 | + | 0.999663i | \(0.491730\pi\) | |||||||
\(410\) | 5.03637e7i | 0.730745i | ||||||||
\(411\) | −9.44081e6 | − | 2.77293e7i | −0.135983 | − | 0.399405i | ||||
\(412\) | 2.23697e7 | 0.319867 | ||||||||
\(413\) | 2.34773e7i | 0.333271i | ||||||||
\(414\) | −5.26045e7 | + | 4.05164e7i | −0.741348 | + | 0.570991i | ||||
\(415\) | 4.93619e7 | 0.690634 | ||||||||
\(416\) | − | 3.38485e7i | − | 0.470175i | ||||||
\(417\) | −1.00304e8 | + | 3.41498e7i | −1.38328 | + | 0.470956i | ||||
\(418\) | 9.78350e7 | 1.33957 | ||||||||
\(419\) | − | 6.97645e7i | − | 0.948402i | −0.880417 | − | 0.474201i | \(-0.842737\pi\) | ||
0.880417 | − | 0.474201i | \(-0.157263\pi\) | |||||||
\(420\) | −4.71752e6 | − | 1.38561e7i | −0.0636745 | − | 0.187023i | ||||
\(421\) | −9.88875e7 | −1.32524 | −0.662621 | − | 0.748955i | \(-0.730556\pi\) | ||||
−0.662621 | + | 0.748955i | \(0.730556\pi\) | |||||||
\(422\) | − | 1.04035e8i | − | 1.38434i | ||||||
\(423\) | 1.24826e7 | + | 1.62068e7i | 0.164924 | + | 0.214130i | ||||
\(424\) | 6.92254e7 | 0.908171 | ||||||||
\(425\) | 3.17283e7i | 0.413314i | ||||||||
\(426\) | 6.63216e7 | − | 2.25801e7i | 0.857879 | − | 0.292077i | ||||
\(427\) | 3.89816e7 | 0.500699 | ||||||||
\(428\) | 4.20527e7i | 0.536367i | ||||||||
\(429\) | −1.93061e7 | − | 5.67052e7i | −0.244524 | − | 0.718209i | ||||
\(430\) | −1.16383e8 | −1.46381 | ||||||||
\(431\) | − | 6.40790e7i | − | 0.800358i | −0.916437 | − | 0.400179i | \(-0.868948\pi\) | ||
0.916437 | − | 0.400179i | \(-0.131052\pi\) | |||||||
\(432\) | −1.53273e7 | + | 2.30742e7i | −0.190114 | + | 0.286204i | ||||
\(433\) | −5.28195e7 | −0.650624 | −0.325312 | − | 0.945607i | \(-0.605469\pi\) | ||||
−0.325312 | + | 0.945607i | \(0.605469\pi\) | |||||||
\(434\) | − | 1.57421e7i | − | 0.192572i | ||||||
\(435\) | −6.30262e7 | + | 2.14581e7i | −0.765690 | + | 0.260690i | ||||
\(436\) | −1.27022e7 | −0.153256 | ||||||||
\(437\) | − | 1.44190e8i | − | 1.72779i | ||||||
\(438\) | 2.57071e6 | + | 7.55061e6i | 0.0305936 | + | 0.0898586i | ||||
\(439\) | 4.94450e7 | 0.584425 | 0.292212 | − | 0.956353i | \(-0.405609\pi\) | ||||
0.292212 | + | 0.956353i | \(0.405609\pi\) | |||||||
\(440\) | 1.40176e8i | 1.64557i | ||||||||
\(441\) | 9.70689e6 | − | 7.47631e6i | 0.113179 | − | 0.0871709i | ||||
\(442\) | −4.49190e7 | −0.520192 | ||||||||
\(443\) | 1.12773e8i | 1.29716i | 0.761146 | + | 0.648581i | \(0.224637\pi\) | ||||
−0.761146 | + | 0.648581i | \(0.775363\pi\) | |||||||
\(444\) | 6.26222e6 | − | 2.13206e6i | 0.0715450 | − | 0.0243585i | ||||
\(445\) | −1.19124e8 | −1.35183 | ||||||||
\(446\) | 1.29914e7i | 0.146437i | ||||||||
\(447\) | 1.88524e7 | + | 5.53728e7i | 0.211079 | + | 0.619975i | ||||
\(448\) | −3.23185e7 | −0.359433 | ||||||||
\(449\) | 3.16029e7i | 0.349131i | 0.984646 | + | 0.174565i | \(0.0558521\pi\) | ||||
−0.984646 | + | 0.174565i | \(0.944148\pi\) | |||||||
\(450\) | −1.38718e7 | − | 1.80104e7i | −0.152228 | − | 0.197646i | ||||
\(451\) | −1.03694e8 | −1.13038 | ||||||||
\(452\) | − | 3.77921e7i | − | 0.409248i | ||||||
\(453\) | 1.10892e8 | − | 3.77546e7i | 1.19290 | − | 0.406140i | ||||
\(454\) | 7.16172e7 | 0.765331 | ||||||||
\(455\) | 2.35898e7i | 0.250432i | ||||||||
\(456\) | −4.48954e7 | − | 1.31865e8i | −0.473486 | − | 1.39071i | ||||
\(457\) | −8.46468e7 | −0.886874 | −0.443437 | − | 0.896305i | \(-0.646241\pi\) | ||||
−0.443437 | + | 0.896305i | \(0.646241\pi\) | |||||||
\(458\) | 2.58526e7i | 0.269097i | ||||||||
\(459\) | −9.87857e7 | − | 6.56193e7i | −1.02154 | − | 0.678568i | ||||
\(460\) | 6.43167e7 | 0.660770 | ||||||||
\(461\) | 1.14018e8i | 1.16377i | 0.813269 | + | 0.581887i | \(0.197686\pi\) | ||||
−0.813269 | + | 0.581887i | \(0.802314\pi\) | |||||||
\(462\) | −3.45801e7 | + | 1.17733e7i | −0.350671 | + | 0.119391i | ||||
\(463\) | 1.13239e8 | 1.14092 | 0.570458 | − | 0.821327i | \(-0.306766\pi\) | ||||
0.570458 | + | 0.821327i | \(0.306766\pi\) | |||||||
\(464\) | 2.40103e7i | 0.240350i | ||||||||
\(465\) | 2.57903e7 | + | 7.57504e7i | 0.256506 | + | 0.753401i | ||||
\(466\) | −4.13224e7 | −0.408346 | ||||||||
\(467\) | − | 1.45343e7i | − | 0.142706i | −0.997451 | − | 0.0713530i | \(-0.977268\pi\) | ||
0.997451 | − | 0.0713530i | \(-0.0227317\pi\) | |||||||
\(468\) | −2.10359e7 | + | 1.62020e7i | −0.205222 | + | 0.158063i | ||||
\(469\) | 4.07158e7 | 0.394679 | ||||||||
\(470\) | 2.40185e7i | 0.231341i | ||||||||
\(471\) | 1.35585e8 | − | 4.61617e7i | 1.29762 | − | 0.441793i | ||||
\(472\) | −9.96607e7 | −0.947759 | ||||||||
\(473\) | − | 2.39621e8i | − | 2.26434i | ||||||
\(474\) | 2.60568e7 | + | 7.65334e7i | 0.244673 | + | 0.718647i | ||||
\(475\) | 4.93670e7 | 0.460634 | ||||||||
\(476\) | − | 2.25989e7i | − | 0.209539i | ||||||
\(477\) | −5.59552e7 | − | 7.26497e7i | −0.515568 | − | 0.669389i | ||||
\(478\) | 7.76172e7 | 0.710680 | ||||||||
\(479\) | 1.15987e8i | 1.05536i | 0.849442 | + | 0.527681i | \(0.176939\pi\) | ||||
−0.849442 | + | 0.527681i | \(0.823061\pi\) | |||||||
\(480\) | 9.93268e7 | − | 3.38172e7i | 0.898137 | − | 0.305783i | ||||
\(481\) | −1.06613e7 | −0.0958021 | ||||||||
\(482\) | 3.20741e7i | 0.286427i | ||||||||
\(483\) | 1.73516e7 | + | 5.09645e7i | 0.153992 | + | 0.452300i | ||||
\(484\) | −3.85962e7 | −0.340415 | ||||||||
\(485\) | 2.06359e7i | 0.180883i | ||||||||
\(486\) | 8.47644e7 | − | 5.94105e6i | 0.738422 | − | 0.0517553i | ||||
\(487\) | 5.67850e7 | 0.491639 | 0.245820 | − | 0.969316i | \(-0.420943\pi\) | ||||
0.245820 | + | 0.969316i | \(0.420943\pi\) | |||||||
\(488\) | 1.65477e8i | 1.42389i | ||||||||
\(489\) | 1.17232e8 | − | 3.99132e7i | 1.00258 | − | 0.341342i | ||||
\(490\) | 1.43856e7 | 0.122276 | ||||||||
\(491\) | − | 1.15095e7i | − | 0.0972326i | −0.998818 | − | 0.0486163i | \(-0.984519\pi\) | ||
0.998818 | − | 0.0486163i | \(-0.0154812\pi\) | |||||||
\(492\) | 1.48139e7 | + | 4.35109e7i | 0.124387 | + | 0.365345i | ||||
\(493\) | −1.02793e8 | −0.857875 | ||||||||
\(494\) | 6.98909e7i | 0.579749i | ||||||||
\(495\) | 1.47110e8 | − | 1.13305e8i | 1.21291 | − | 0.934188i | ||||
\(496\) | 2.88577e7 | 0.236492 | ||||||||
\(497\) | − | 5.68059e7i | − | 0.462726i | ||||||
\(498\) | −5.16916e7 | + | 1.75991e7i | −0.418535 | + | 0.142496i | ||||
\(499\) | 9.78927e7 | 0.787859 | 0.393930 | − | 0.919141i | \(-0.371115\pi\) | ||||
0.393930 | + | 0.919141i | \(0.371115\pi\) | |||||||
\(500\) | − | 4.33181e7i | − | 0.346545i | ||||||
\(501\) | 5.42989e7 | + | 1.59485e8i | 0.431795 | + | 1.26826i | ||||
\(502\) | −1.73444e7 | −0.137104 | ||||||||
\(503\) | − | 5.09840e7i | − | 0.400618i | −0.979733 | − | 0.200309i | \(-0.935805\pi\) | ||
0.979733 | − | 0.200309i | \(-0.0641946\pi\) | |||||||
\(504\) | 3.17368e7 | + | 4.12056e7i | 0.247898 | + | 0.321859i | ||||
\(505\) | −9.49177e7 | −0.737010 | ||||||||
\(506\) | − | 1.60512e8i | − | 1.23896i | ||||||
\(507\) | −8.28608e7 | + | 2.82111e7i | −0.635807 | + | 0.216469i | ||||
\(508\) | 6.91337e7 | 0.527350 | ||||||||
\(509\) | − | 5.52683e7i | − | 0.419105i | −0.977797 | − | 0.209553i | \(-0.932799\pi\) | ||
0.977797 | − | 0.209553i | \(-0.0672007\pi\) | |||||||
\(510\) | −4.48774e7 | − | 1.31813e8i | −0.338312 | − | 0.993680i | ||||
\(511\) | 6.46725e6 | 0.0484682 | ||||||||
\(512\) | − | 8.74079e7i | − | 0.651239i | ||||||
\(513\) | −1.02099e8 | + | 1.53704e8i | −0.756258 | + | 1.13850i | ||||
\(514\) | 6.88852e7 | 0.507267 | ||||||||
\(515\) | − | 1.11756e8i | − | 0.818177i | ||||||
\(516\) | −1.00547e8 | + | 3.42326e7i | −0.731847 | + | 0.249167i | ||||
\(517\) | −4.94518e7 | −0.357858 | ||||||||
\(518\) | 6.50150e6i | 0.0467761i | ||||||||
\(519\) | 7.11237e7 | + | 2.08902e8i | 0.508759 | + | 1.49431i | ||||
\(520\) | −1.00138e8 | −0.712182 | ||||||||
\(521\) | 8.63374e7i | 0.610500i | 0.952272 | + | 0.305250i | \(0.0987400\pi\) | ||||
−0.952272 | + | 0.305250i | \(0.901260\pi\) | |||||||
\(522\) | 5.83502e7 | − | 4.49417e7i | 0.410234 | − | 0.315965i | ||||
\(523\) | −1.74938e8 | −1.22287 | −0.611433 | − | 0.791296i | \(-0.709407\pi\) | ||||
−0.611433 | + | 0.791296i | \(0.709407\pi\) | |||||||
\(524\) | − | 6.13163e7i | − | 0.426169i | ||||||
\(525\) | −1.74489e7 | + | 5.94073e6i | −0.120584 | + | 0.0410546i | ||||
\(526\) | −1.22519e8 | −0.841871 | ||||||||
\(527\) | 1.23546e8i | 0.844106i | ||||||||
\(528\) | −2.15823e7 | − | 6.33908e7i | −0.146621 | − | 0.430650i | ||||
\(529\) | −8.85282e7 | −0.598018 | ||||||||
\(530\) | − | 1.07667e8i | − | 0.723192i | ||||||
\(531\) | 8.05563e7 | + | 1.04590e8i | 0.538041 | + | 0.698568i | ||||
\(532\) | −3.51623e7 | −0.233530 | ||||||||
\(533\) | − | 7.40765e7i | − | 0.489214i | ||||||
\(534\) | 1.24747e8 | − | 4.24717e7i | 0.819229 | − | 0.278918i | ||||
\(535\) | 2.10088e8 | 1.37196 | ||||||||
\(536\) | 1.72838e8i | 1.12239i | ||||||||
\(537\) | −6.17922e7 | − | 1.81494e8i | −0.399035 | − | 1.17203i | ||||
\(538\) | −1.72711e8 | −1.10911 | ||||||||
\(539\) | 2.96186e7i | 0.189146i | ||||||||
\(540\) | −6.85603e7 | − | 4.55418e7i | −0.435403 | − | 0.289220i | ||||
\(541\) | −1.59466e8 | −1.00711 | −0.503553 | − | 0.863964i | \(-0.667974\pi\) | ||||
−0.503553 | + | 0.863964i | \(0.667974\pi\) | |||||||
\(542\) | − | 4.37465e7i | − | 0.274755i | ||||||
\(543\) | −1.76930e8 | + | 6.02381e7i | −1.10510 | + | 0.376246i | ||||
\(544\) | 1.61998e8 | 1.00627 | ||||||||
\(545\) | 6.34581e7i | 0.392010i | ||||||||
\(546\) | −8.41053e6 | − | 2.47032e7i | −0.0516708 | − | 0.151766i | ||||
\(547\) | −7.00929e7 | −0.428265 | −0.214132 | − | 0.976805i | \(-0.568692\pi\) | ||||
−0.214132 | + | 0.976805i | \(0.568692\pi\) | |||||||
\(548\) | − | 3.13878e7i | − | 0.190730i | ||||||
\(549\) | 1.73662e8 | − | 1.33756e8i | 1.04951 | − | 0.808342i | ||||
\(550\) | 5.49552e7 | 0.330309 | ||||||||
\(551\) | 1.59939e8i | 0.956094i | ||||||||
\(552\) | −2.16344e8 | + | 7.36572e7i | −1.28625 | + | 0.437923i | ||||
\(553\) | 6.55525e7 | 0.387627 | ||||||||
\(554\) | 1.65309e8i | 0.972226i | ||||||||
\(555\) | −1.06514e7 | − | 3.12851e7i | −0.0623059 | − | 0.183003i | ||||
\(556\) | −1.13538e8 | −0.660564 | ||||||||
\(557\) | 1.25867e8i | 0.728361i | 0.931328 | + | 0.364180i | \(0.118651\pi\) | ||||
−0.931328 | + | 0.364180i | \(0.881349\pi\) | |||||||
\(558\) | −5.40149e7 | − | 7.01305e7i | −0.310893 | − | 0.403649i | ||||
\(559\) | 1.71179e8 | 0.979977 | ||||||||
\(560\) | 2.63711e7i | 0.150163i | ||||||||
\(561\) | 2.71390e8 | − | 9.23983e7i | 1.53711 | − | 0.523330i | ||||
\(562\) | 5.41611e7 | 0.305126 | ||||||||
\(563\) | − | 1.55535e8i | − | 0.871569i | −0.900051 | − | 0.435784i | \(-0.856471\pi\) | ||
0.900051 | − | 0.435784i | \(-0.143529\pi\) | |||||||
\(564\) | 7.06476e6 | + | 2.07504e7i | 0.0393786 | + | 0.115662i | ||||
\(565\) | −1.88804e8 | −1.04680 | ||||||||
\(566\) | − | 1.50512e8i | − | 0.830083i | ||||||
\(567\) | 1.75908e7 | − | 6.66135e7i | 0.0965022 | − | 0.365437i | ||||
\(568\) | 2.41140e8 | 1.31591 | ||||||||
\(569\) | − | 3.14182e8i | − | 1.70547i | −0.522341 | − | 0.852737i | \(-0.674941\pi\) | ||
0.522341 | − | 0.852737i | \(-0.325059\pi\) | |||||||
\(570\) | −2.05091e8 | + | 6.98262e7i | −1.10745 | + | 0.377045i | ||||
\(571\) | 4.88889e7 | 0.262604 | 0.131302 | − | 0.991342i | \(-0.458084\pi\) | ||||
0.131302 | + | 0.991342i | \(0.458084\pi\) | |||||||
\(572\) | − | 6.41867e7i | − | 0.342970i | ||||||
\(573\) | −4.50470e7 | − | 1.32311e8i | −0.239443 | − | 0.703285i | ||||
\(574\) | −4.51735e7 | −0.238863 | ||||||||
\(575\) | − | 8.09935e7i | − | 0.426036i | ||||||
\(576\) | −1.43978e8 | + | 1.10893e8i | −0.753406 | + | 0.580278i | ||||
\(577\) | 2.77649e8 | 1.44533 | 0.722667 | − | 0.691197i | \(-0.242916\pi\) | ||||
0.722667 | + | 0.691197i | \(0.242916\pi\) | |||||||
\(578\) | − | 7.20419e7i | − | 0.373080i | ||||||
\(579\) | −2.04329e8 | + | 6.95667e7i | −1.05268 | + | 0.358398i | ||||
\(580\) | −7.13417e7 | −0.365645 | ||||||||
\(581\) | 4.42750e7i | 0.225751i | ||||||||
\(582\) | −7.35737e6 | − | 2.16098e7i | −0.0373210 | − | 0.109618i | ||||
\(583\) | 2.21675e8 | 1.11870 | ||||||||
\(584\) | 2.74534e7i | 0.137834i | ||||||||
\(585\) | 8.09425e7 | + | 1.05092e8i | 0.404305 | + | 0.524930i | ||||
\(586\) | 8.21665e7 | 0.408321 | ||||||||
\(587\) | 2.10445e7i | 0.104046i | 0.998646 | + | 0.0520230i | \(0.0165669\pi\) | ||||
−0.998646 | + | 0.0520230i | \(0.983433\pi\) | |||||||
\(588\) | 1.24282e7 | − | 4.23136e6i | 0.0611331 | − | 0.0208136i | ||||
\(589\) | 1.92229e8 | 0.940748 | ||||||||
\(590\) | 1.55003e8i | 0.754717i | ||||||||
\(591\) | 2.95858e7 | + | 8.68984e7i | 0.143324 | + | 0.420968i | ||||
\(592\) | −1.19183e7 | −0.0574446 | ||||||||
\(593\) | 2.99569e8i | 1.43659i | 0.695739 | + | 0.718295i | \(0.255077\pi\) | ||||
−0.695739 | + | 0.718295i | \(0.744923\pi\) | |||||||
\(594\) | −1.13656e8 | + | 1.71102e8i | −0.542293 | + | 0.816388i | ||||
\(595\) | −1.12900e8 | −0.535975 | ||||||||
\(596\) | 6.26786e7i | 0.296060i | ||||||||
\(597\) | −1.85713e8 | + | 6.32285e7i | −0.872808 | + | 0.297159i | ||||
\(598\) | 1.14666e8 | 0.536204 | ||||||||
\(599\) | 2.59759e8i | 1.20862i | 0.796748 | + | 0.604312i | \(0.206552\pi\) | ||||
−0.796748 | + | 0.604312i | \(0.793448\pi\) | |||||||
\(600\) | −2.52183e7 | − | 7.40705e7i | −0.116752 | − | 0.342919i | ||||
\(601\) | 7.52160e6 | 0.0346487 | 0.0173243 | − | 0.999850i | \(-0.494485\pi\) | ||||
0.0173243 | + | 0.999850i | \(0.494485\pi\) | |||||||
\(602\) | − | 1.04389e8i | − | 0.478482i | ||||||
\(603\) | 1.81387e8 | − | 1.39706e8i | 0.827285 | − | 0.637181i | ||||
\(604\) | 1.25523e8 | 0.569654 | ||||||||
\(605\) | 1.92821e8i | 0.870737i | ||||||||
\(606\) | 9.93974e7 | − | 3.38412e7i | 0.446640 | − | 0.152065i | ||||
\(607\) | −8.22850e7 | −0.367921 | −0.183961 | − | 0.982934i | \(-0.558892\pi\) | ||||
−0.183961 | + | 0.982934i | \(0.558892\pi\) | |||||||
\(608\) | − | 2.52058e8i | − | 1.12148i | ||||||
\(609\) | −1.92468e7 | − | 5.65311e7i | −0.0852131 | − | 0.250285i | ||||
\(610\) | 2.57367e8 | 1.13387 | ||||||||
\(611\) | − | 3.53271e7i | − | 0.154876i | ||||||
\(612\) | −7.75423e7 | − | 1.00677e8i | −0.338286 | − | 0.439215i | ||||
\(613\) | −2.05993e7 | −0.0894277 | −0.0447138 | − | 0.999000i | \(-0.514238\pi\) | ||||
−0.0447138 | + | 0.999000i | \(0.514238\pi\) | |||||||
\(614\) | − | 1.26650e7i | − | 0.0547141i | ||||||
\(615\) | 2.17374e8 | − | 7.40079e7i | 0.934505 | − | 0.318165i | ||||
\(616\) | −1.25731e8 | −0.537896 | ||||||||
\(617\) | 2.59281e8i | 1.10386i | 0.833889 | + | 0.551932i | \(0.186109\pi\) | ||||
−0.833889 | + | 0.551932i | \(0.813891\pi\) | |||||||
\(618\) | 3.98445e7 | + | 1.17030e8i | 0.168812 | + | 0.495829i | ||||
\(619\) | 2.09715e8 | 0.884212 | 0.442106 | − | 0.896963i | \(-0.354231\pi\) | ||||
0.442106 | + | 0.896963i | \(0.354231\pi\) | |||||||
\(620\) | 8.57447e7i | 0.359776i | ||||||||
\(621\) | 2.52172e8 | + | 1.67508e8i | 1.05299 | + | 0.699455i | ||||
\(622\) | 1.30544e8 | 0.542481 | ||||||||
\(623\) | − | 1.06848e8i | − | 0.441879i | ||||||
\(624\) | 4.52848e7 | − | 1.54179e7i | 0.186380 | − | 0.0634556i | ||||
\(625\) | −2.98691e8 | −1.22344 | ||||||||
\(626\) | 4.45746e7i | 0.181704i | ||||||||
\(627\) | −1.43765e8 | − | 4.22263e8i | −0.583246 | − | 1.71309i | ||||
\(628\) | 1.53473e8 | 0.619661 | ||||||||
\(629\) | − | 5.10247e7i | − | 0.205035i | ||||||
\(630\) | 6.40874e7 | − | 4.93606e7i | 0.256302 | − | 0.197405i | ||||
\(631\) | −1.33312e8 | −0.530615 | −0.265308 | − | 0.964164i | \(-0.585473\pi\) | ||||
−0.265308 | + | 0.964164i | \(0.585473\pi\) | |||||||
\(632\) | 2.78269e8i | 1.10234i | ||||||||
\(633\) | −4.49023e8 | + | 1.52876e8i | −1.77034 | + | 0.602737i | ||||
\(634\) | −6.56198e7 | −0.257494 | ||||||||
\(635\) | − | 3.45381e8i | − | 1.34889i | ||||||
\(636\) | −3.16689e7 | − | 9.30169e7i | −0.123101 | − | 0.361569i | ||||
\(637\) | −2.11588e7 | −0.0818601 | ||||||||
\(638\) | 1.78044e8i | 0.685590i | ||||||||
\(639\) | −1.94915e8 | − | 2.53068e8i | −0.747038 | − | 0.969919i | ||||
\(640\) | 3.53374e7 | 0.134801 | ||||||||
\(641\) | − | 3.80864e8i | − | 1.44609i | −0.690801 | − | 0.723045i | \(-0.742742\pi\) | ||
0.690801 | − | 0.723045i | \(-0.257258\pi\) | |||||||
\(642\) | −2.20004e8 | + | 7.49033e7i | −0.831429 | + | 0.283071i | ||||
\(643\) | −3.98844e8 | −1.50027 | −0.750136 | − | 0.661284i | \(-0.770012\pi\) | ||||
−0.750136 | + | 0.661284i | \(0.770012\pi\) | |||||||
\(644\) | 5.76886e7i | 0.215989i | ||||||||
\(645\) | 1.71021e8 | + | 5.02317e8i | 0.637338 | + | 1.87197i | ||||
\(646\) | −3.34496e8 | −1.24078 | ||||||||
\(647\) | − | 2.61564e8i | − | 0.965752i | −0.875689 | − | 0.482876i | \(-0.839592\pi\) | ||
0.875689 | − | 0.482876i | \(-0.160408\pi\) | |||||||
\(648\) | 2.82773e8 | + | 7.46729e7i | 1.03923 | + | 0.274434i | ||||
\(649\) | −3.19136e8 | −1.16746 | ||||||||
\(650\) | 3.92586e7i | 0.142954i | ||||||||
\(651\) | −6.79440e7 | + | 2.31325e7i | −0.246268 | + | 0.0838454i | ||||
\(652\) | 1.32699e8 | 0.478768 | ||||||||
\(653\) | − | 5.21308e8i | − | 1.87221i | −0.351718 | − | 0.936106i | \(-0.614402\pi\) | ||
0.351718 | − | 0.936106i | \(-0.385598\pi\) | |||||||
\(654\) | −2.26249e7 | − | 6.64530e7i | −0.0808821 | − | 0.237565i | ||||
\(655\) | −3.06326e8 | −1.09009 | ||||||||
\(656\) | − | 8.28103e7i | − | 0.293341i | ||||||
\(657\) | 2.88114e7 | − | 2.21907e7i | 0.101594 | − | 0.0782485i | ||||
\(658\) | −2.15433e7 | −0.0756196 | ||||||||
\(659\) | − | 3.49679e8i | − | 1.22184i | −0.791694 | − | 0.610918i | \(-0.790800\pi\) | ||
0.791694 | − | 0.610918i | \(-0.209200\pi\) | |||||||
\(660\) | 1.88353e8 | − | 6.41272e7i | 0.655148 | − | 0.223054i | ||||
\(661\) | 2.26886e8 | 0.785602 | 0.392801 | − | 0.919624i | \(-0.371506\pi\) | ||||
0.392801 | + | 0.919624i | \(0.371506\pi\) | |||||||
\(662\) | − | 1.86735e8i | − | 0.643654i | ||||||
\(663\) | 6.60071e7 | + | 1.93874e8i | 0.226490 | + | 0.665241i | ||||
\(664\) | −1.87947e8 | −0.641993 | ||||||||
\(665\) | 1.75665e8i | 0.597338i | ||||||||
\(666\) | 2.23083e7 | + | 2.89640e7i | 0.0755167 | + | 0.0980474i | ||||
\(667\) | 2.62403e8 | 0.884282 | ||||||||
\(668\) | 1.80527e8i | 0.605638i | ||||||||
\(669\) | 5.60718e7 | − | 1.90904e7i | 0.187269 | − | 0.0637584i | ||||
\(670\) | 2.68816e8 | 0.893780 | ||||||||
\(671\) | 5.29894e8i | 1.75397i | ||||||||
\(672\) | 3.03322e7 | + | 8.90907e7i | 0.0999529 | + | 0.293579i | ||||
\(673\) | −2.64148e8 | −0.866565 | −0.433283 | − | 0.901258i | \(-0.642645\pi\) | ||||
−0.433283 | + | 0.901258i | \(0.642645\pi\) | |||||||
\(674\) | 2.03333e8i | 0.664091i | ||||||||
\(675\) | −5.73504e7 | + | 8.63374e7i | −0.186477 | + | 0.280729i | ||||
\(676\) | −9.37933e7 | −0.303621 | ||||||||
\(677\) | − | 3.84404e8i | − | 1.23886i | −0.785052 | − | 0.619429i | \(-0.787364\pi\) | ||
0.785052 | − | 0.619429i | \(-0.212636\pi\) | |||||||
\(678\) | 1.97714e8 | − | 6.73146e7i | 0.634379 | − | 0.215983i | ||||
\(679\) | −1.85093e7 | −0.0591262 | ||||||||
\(680\) | − | 4.79260e8i | − | 1.52421i | ||||||
\(681\) | −1.05239e8 | − | 3.09105e8i | −0.333224 | − | 0.978735i | ||||
\(682\) | 2.13989e8 | 0.674587 | ||||||||
\(683\) | 5.31494e8i | 1.66816i | 0.551647 | + | 0.834078i | \(0.313999\pi\) | ||||
−0.551647 | + | 0.834078i | \(0.686001\pi\) | |||||||
\(684\) | −1.56647e8 | + | 1.20650e8i | −0.489501 | + | 0.377017i | ||||
\(685\) | −1.56808e8 | −0.487863 | ||||||||
\(686\) | 1.29031e7i | 0.0399689i | ||||||||
\(687\) | 1.11582e8 | − | 3.79896e7i | 0.344131 | − | 0.117164i | ||||
\(688\) | 1.91362e8 | 0.587611 | ||||||||
\(689\) | 1.58359e8i | 0.484157i | ||||||||
\(690\) | 1.14560e8 | + | 3.36481e8i | 0.348726 | + | 1.02427i | ||||
\(691\) | −3.70050e8 | −1.12157 | −0.560784 | − | 0.827962i | \(-0.689500\pi\) | ||||
−0.560784 | + | 0.827962i | \(0.689500\pi\) | |||||||
\(692\) | 2.36464e8i | 0.713588i | ||||||||
\(693\) | 1.01629e8 | + | 1.31950e8i | 0.305363 | + | 0.396469i | ||||
\(694\) | −3.22110e8 | −0.963664 | ||||||||
\(695\) | 5.67216e8i | 1.68964i | ||||||||
\(696\) | 2.39974e8 | − | 8.17023e7i | 0.711764 | − | 0.242330i | ||||
\(697\) | 3.54528e8 | 1.04701 | ||||||||
\(698\) | − | 5.90098e7i | − | 0.173523i | ||||||
\(699\) | 6.07220e7 | + | 1.78351e8i | 0.177793 | + | 0.522208i | ||||
\(700\) | −1.97511e7 | −0.0575834 | ||||||||
\(701\) | 2.97612e8i | 0.863965i | 0.901882 | + | 0.431982i | \(0.142186\pi\) | ||||
−0.901882 | + | 0.431982i | \(0.857814\pi\) | |||||||
\(702\) | −1.22231e8 | − | 8.11932e7i | −0.353322 | − | 0.234698i | ||||
\(703\) | −7.93910e7 | −0.228510 | ||||||||
\(704\) | − | 4.39320e8i | − | 1.25911i | ||||||
\(705\) | 1.03666e8 | − | 3.52944e7i | 0.295847 | − | 0.100725i | ||||
\(706\) | −4.33141e8 | −1.23088 | ||||||||
\(707\) | − | 8.51360e7i | − | 0.240910i | ||||||
\(708\) | 4.55923e7 | + | 1.33912e8i | 0.128467 | + | 0.377330i | ||||
\(709\) | 3.42752e8 | 0.961704 | 0.480852 | − | 0.876802i | \(-0.340328\pi\) | ||||
0.480852 | + | 0.876802i | \(0.340328\pi\) | |||||||
\(710\) | − | 3.75047e8i | − | 1.04788i | ||||||
\(711\) | 2.92034e8 | − | 2.24927e8i | 0.812503 | − | 0.625795i | ||||
\(712\) | 4.53569e8 | 1.25662 | ||||||||
\(713\) | − | 3.15379e8i | − | 0.870089i | ||||||
\(714\) | 1.18229e8 | − | 4.02526e7i | 0.324809 | − | 0.110586i | ||||
\(715\) | −3.20666e8 | −0.877274 | ||||||||
\(716\) | − | 2.05440e8i | − | 0.559688i | ||||||
\(717\) | −1.14056e8 | − | 3.35002e8i | −0.309429 | − | 0.908845i | ||||
\(718\) | 1.18150e8 | 0.319199 | ||||||||
\(719\) | − | 1.85318e8i | − | 0.498576i | −0.968429 | − | 0.249288i | \(-0.919803\pi\) | ||
0.968429 | − | 0.249288i | \(-0.0801966\pi\) | |||||||
\(720\) | 9.04858e7 | + | 1.17483e8i | 0.242428 | + | 0.314757i | ||||
\(721\) | 1.00239e8 | 0.267442 | ||||||||
\(722\) | 2.41853e8i | 0.642600i | ||||||||
\(723\) | 1.38434e8 | − | 4.71319e7i | 0.366293 | − | 0.124710i | ||||
\(724\) | −2.00273e8 | −0.527724 | ||||||||
\(725\) | 8.98400e7i | 0.235752i | ||||||||
\(726\) | −6.87467e7 | − | 2.01921e8i | −0.179656 | − | 0.527681i | ||||
\(727\) | 4.21828e8 | 1.09782 | 0.548912 | − | 0.835880i | \(-0.315042\pi\) | ||||
0.548912 | + | 0.835880i | \(0.315042\pi\) | |||||||
\(728\) | − | 8.98188e7i | − | 0.232795i | ||||||
\(729\) | −1.50201e8 | − | 3.57120e8i | −0.387694 | − | 0.921788i | ||||
\(730\) | 4.26985e7 | 0.109760 | ||||||||
\(731\) | 8.19260e8i | 2.09734i | ||||||||
\(732\) | 2.22348e8 | − | 7.57015e7i | 0.566892 | − | 0.193006i | ||||
\(733\) | 3.71133e8 | 0.942362 | 0.471181 | − | 0.882036i | \(-0.343828\pi\) | ||||
0.471181 | + | 0.882036i | \(0.343828\pi\) | |||||||
\(734\) | 1.17113e7i | 0.0296154i | ||||||||
\(735\) | −2.11392e7 | − | 6.20894e7i | −0.0532385 | − | 0.156371i | ||||
\(736\) | −4.13536e8 | −1.03724 | ||||||||
\(737\) | 5.53467e8i | 1.38258i | ||||||||
\(738\) | −2.01247e8 | + | 1.55001e8i | −0.500679 | + | 0.385626i | ||||
\(739\) | −6.21470e8 | −1.53988 | −0.769940 | − | 0.638116i | \(-0.779714\pi\) | ||||
−0.769940 | + | 0.638116i | \(0.779714\pi\) | |||||||
\(740\) | − | 3.54127e7i | − | 0.0873904i | ||||||
\(741\) | 3.01655e8 | − | 1.02702e8i | 0.741405 | − | 0.252421i | ||||
\(742\) | 9.65712e7 | 0.236394 | ||||||||
\(743\) | − | 7.90305e7i | − | 0.192676i | −0.995349 | − | 0.0963382i | \(-0.969287\pi\) | ||
0.995349 | − | 0.0963382i | \(-0.0307130\pi\) | |||||||
\(744\) | −9.81971e7 | − | 2.88422e8i | −0.238440 | − | 0.700340i | ||||
\(745\) | 3.13132e8 | 0.757284 | ||||||||
\(746\) | 1.55230e8i | 0.373903i | ||||||||
\(747\) | 1.51918e8 | + | 1.97244e8i | 0.364459 | + | 0.473196i | ||||
\(748\) | 3.07196e8 | 0.734025 | ||||||||
\(749\) | 1.88438e8i | 0.448459i | ||||||||
\(750\) | 2.26624e8 | − | 7.71573e7i | 0.537183 | − | 0.182891i | ||||
\(751\) | 7.00643e8 | 1.65416 | 0.827079 | − | 0.562086i | \(-0.190001\pi\) | ||||
0.827079 | + | 0.562086i | \(0.190001\pi\) | |||||||
\(752\) | − | 3.94923e7i | − | 0.0928665i | ||||||
\(753\) | 2.54871e7 | + | 7.48599e7i | 0.0596946 | + | 0.175333i | ||||
\(754\) | −1.27190e8 | −0.296715 | ||||||||
\(755\) | − | 6.27091e8i | − | 1.45710i | ||||||
\(756\) | 4.08485e7 | − | 6.14948e7i | 0.0945389 | − | 0.142322i | ||||
\(757\) | −2.45843e8 | −0.566722 | −0.283361 | − | 0.959013i | \(-0.591449\pi\) | ||||
−0.283361 | + | 0.959013i | \(0.591449\pi\) | |||||||
\(758\) | 3.09020e8i | 0.709544i | ||||||||
\(759\) | −6.92782e8 | + | 2.35867e8i | −1.58442 | + | 0.539439i | ||||
\(760\) | −7.45696e8 | −1.69872 | ||||||||
\(761\) | 1.11614e8i | 0.253258i | 0.991950 | + | 0.126629i | \(0.0404158\pi\) | ||||
−0.991950 | + | 0.126629i | \(0.959584\pi\) | |||||||
\(762\) | 1.23139e8 | + | 3.61681e8i | 0.278312 | + | 0.817450i | ||||
\(763\) | −5.69184e7 | −0.128138 | ||||||||
\(764\) | − | 1.49767e8i | − | 0.335844i | ||||||
\(765\) | −5.02968e8 | + | 3.87389e8i | −1.12345 | + | 0.865292i | ||||
\(766\) | −2.42020e8 | −0.538475 | ||||||||
\(767\) | − | 2.27983e8i | − | 0.505262i | ||||||
\(768\) | −4.44793e8 | + | 1.51436e8i | −0.981917 | + | 0.334307i | ||||
\(769\) | 1.31906e8 | 0.290059 | 0.145030 | − | 0.989427i | \(-0.453672\pi\) | ||||
0.145030 | + | 0.989427i | \(0.453672\pi\) | |||||||
\(770\) | 1.95550e8i | 0.428336i | ||||||||
\(771\) | −1.01225e8 | − | 2.97314e8i | −0.220863 | − | 0.648713i | ||||
\(772\) | −2.31288e8 | −0.502691 | ||||||||
\(773\) | − | 5.26599e8i | − | 1.14010i | −0.821611 | − | 0.570048i | \(-0.806924\pi\) | ||
0.821611 | − | 0.570048i | \(-0.193076\pi\) | |||||||
\(774\) | −3.58184e8 | − | 4.65050e8i | −0.772474 | − | 1.00294i | ||||
\(775\) | 1.07978e8 | 0.231968 | ||||||||
\(776\) | − | 7.85717e7i | − | 0.168144i | ||||||
\(777\) | 2.80610e7 | − | 9.55375e6i | 0.0598191 | − | 0.0203662i | ||||
\(778\) | −3.57345e8 | −0.758837 | ||||||||
\(779\) | − | 5.51621e8i | − | 1.16689i | ||||||
\(780\) | 4.58109e7 | + | 1.34554e8i | 0.0965350 | + | 0.283540i | ||||
\(781\) | 7.72186e8 | 1.62095 | ||||||||
\(782\) | 5.48788e8i | 1.14758i | ||||||||
\(783\) | −2.79716e8 | − | 1.85804e8i | −0.582682 | − | 0.387052i | ||||
\(784\) | −2.36535e7 | −0.0490847 | ||||||||
\(785\) | − | 7.66729e8i | − | 1.58501i | ||||||
\(786\) | 3.20784e8 | − | 1.09215e8i | 0.660609 | − | 0.224914i | ||||
\(787\) | −2.05228e8 | −0.421029 | −0.210515 | − | 0.977591i | \(-0.567514\pi\) | ||||
−0.210515 | + | 0.977591i | \(0.567514\pi\) | |||||||
\(788\) | 9.83635e7i | 0.201028i | ||||||||
\(789\) | 1.80037e8 | + | 5.28801e8i | 0.366549 | + | 1.07662i | ||||
\(790\) | 4.32795e8 | 0.877810 | ||||||||
\(791\) | − | 1.69347e8i | − | 0.342174i | ||||||
\(792\) | −5.60126e8 | + | 4.31412e8i | −1.12748 | + | 0.868395i | ||||
\(793\) | −3.78543e8 | −0.759095 | ||||||||
\(794\) | − | 1.35099e8i | − | 0.269892i | ||||||
\(795\) | −4.64698e8 | + | 1.58213e8i | −0.924846 | + | 0.314876i | ||||
\(796\) | −2.10215e8 | −0.416797 | ||||||||
\(797\) | 5.91897e8i | 1.16915i | 0.811339 | + | 0.584576i | \(0.198739\pi\) | ||||
−0.811339 | + | 0.584576i | \(0.801261\pi\) | |||||||
\(798\) | −6.26303e7 | − | 1.83956e8i | −0.123247 | − | 0.361997i | ||||
\(799\) | 1.69075e8 | 0.331466 | ||||||||
\(800\) | − | 1.41584e8i | − | 0.276532i | ||||||
\(801\) | −3.66622e8 | − | 4.76005e8i | −0.713381 | − | 0.926220i | ||||
\(802\) | −1.02923e8 | −0.199521 | ||||||||
\(803\) | 8.79121e7i | 0.169786i | ||||||||
\(804\) | 2.32239e8 | − | 7.90691e7i | 0.446856 | − | 0.152138i | ||||
\(805\) | 2.88203e8 | 0.552473 | ||||||||
\(806\) | 1.52868e8i | 0.291952i | ||||||||
\(807\) | 2.53794e8 | + | 7.45435e8i | 0.482903 | + | 1.41837i | ||||
\(808\) | 3.61401e8 | 0.685103 | ||||||||
\(809\) | 4.63734e8i | 0.875837i | 0.899015 | + | 0.437919i | \(0.144284\pi\) | ||||
−0.899015 | + | 0.437919i | \(0.855716\pi\) | |||||||
\(810\) | 1.16139e8 | − | 4.39800e8i | 0.218537 | − | 0.827561i | ||||
\(811\) | −2.00773e8 | −0.376395 | −0.188197 | − | 0.982131i | \(-0.560264\pi\) | ||||
−0.188197 | + | 0.982131i | \(0.560264\pi\) | |||||||
\(812\) | − | 6.39896e7i | − | 0.119520i | ||||||
\(813\) | −1.88813e8 | + | 6.42841e7i | −0.351367 | + | 0.119628i | ||||
\(814\) | −8.83777e7 | −0.163859 | ||||||||
\(815\) | − | 6.62944e8i | − | 1.22463i | ||||||
\(816\) | 7.37895e7 | + | 2.16732e8i | 0.135808 | + | 0.398890i | ||||
\(817\) | 1.27471e9 | 2.33747 | ||||||||
\(818\) | 2.10510e7i | 0.0384603i | ||||||||
\(819\) | −9.42617e7 | + | 7.26010e7i | −0.171587 | + | 0.132157i | ||||
\(820\) | 2.46053e8 | 0.446260 | ||||||||
\(821\) | − | 3.61647e8i | − | 0.653515i | −0.945108 | − | 0.326758i | \(-0.894044\pi\) | ||
0.945108 | − | 0.326758i | \(-0.105956\pi\) | |||||||
\(822\) | 1.64209e8 | − | 5.59073e7i | 0.295653 | − | 0.100659i | ||||
\(823\) | −2.84708e8 | −0.510740 | −0.255370 | − | 0.966843i | \(-0.582197\pi\) | ||||
−0.255370 | + | 0.966843i | \(0.582197\pi\) | |||||||
\(824\) | 4.25512e8i | 0.760554i | ||||||||
\(825\) | −8.07549e7 | − | 2.37191e8i | −0.143816 | − | 0.422412i | ||||
\(826\) | −1.39029e8 | −0.246698 | ||||||||
\(827\) | 3.63770e7i | 0.0643147i | 0.999483 | + | 0.0321574i | \(0.0102378\pi\) | ||||
−0.999483 | + | 0.0321574i | \(0.989762\pi\) | |||||||
\(828\) | 1.97944e8 | + | 2.57001e8i | 0.348699 | + | 0.452735i | ||||
\(829\) | 2.91940e8 | 0.512425 | 0.256212 | − | 0.966621i | \(-0.417525\pi\) | ||||
0.256212 | + | 0.966621i | \(0.417525\pi\) | |||||||
\(830\) | 2.92315e8i | 0.511230i | ||||||||
\(831\) | 7.13486e8 | − | 2.42916e8i | 1.24332 | − | 0.423305i | ||||
\(832\) | 3.13839e8 | 0.544925 | ||||||||
\(833\) | − | 1.01265e8i | − | 0.175197i | ||||||
\(834\) | −2.02231e8 | − | 5.93986e8i | −0.348617 | − | 1.02395i | ||||
\(835\) | 9.01884e8 | 1.54914 | ||||||||
\(836\) | − | 4.77976e8i | − | 0.818063i | ||||||
\(837\) | −2.23315e8 | + | 3.36187e8i | −0.380840 | + | 0.573330i | ||||
\(838\) | 4.13136e8 | 0.702039 | ||||||||
\(839\) | 4.25640e7i | 0.0720703i | 0.999351 | + | 0.0360351i | \(0.0114728\pi\) | ||||
−0.999351 | + | 0.0360351i | \(0.988527\pi\) | |||||||
\(840\) | 2.63569e8 | − | 8.97356e7i | 0.444689 | − | 0.151400i | ||||
\(841\) | 3.03760e8 | 0.510672 | ||||||||
\(842\) | − | 5.85599e8i | − | 0.980989i | ||||||
\(843\) | −7.95881e7 | − | 2.33764e8i | −0.132851 | − | 0.390206i | ||||
\(844\) | −5.08265e8 | −0.845402 | ||||||||
\(845\) | 4.68576e8i | 0.776623i | ||||||||
\(846\) | −9.59747e7 | + | 7.39203e7i | −0.158506 | + | 0.122082i | ||||
\(847\) | −1.72950e8 | −0.284622 | ||||||||
\(848\) | 1.77030e8i | 0.290309i | ||||||||
\(849\) | −6.49621e8 | + | 2.21172e8i | −1.06154 | + | 0.361416i | ||||
\(850\) | −1.87891e8 | −0.305949 | ||||||||
\(851\) | 1.30252e8i | 0.211347i | ||||||||
\(852\) | −1.10316e8 | − | 3.24016e8i | −0.178369 | − | 0.523899i | ||||
\(853\) | −2.80622e8 | −0.452142 | −0.226071 | − | 0.974111i | \(-0.572588\pi\) | ||||
−0.226071 | + | 0.974111i | \(0.572588\pi\) | |||||||
\(854\) | 2.30844e8i | 0.370634i | ||||||||
\(855\) | 6.02750e8 | + | 7.82583e8i | 0.964360 | + | 1.25208i | ||||
\(856\) | −7.99917e8 | −1.27533 | ||||||||
\(857\) | 9.46806e8i | 1.50424i | 0.659023 | + | 0.752122i | \(0.270970\pi\) | ||||
−0.659023 | + | 0.752122i | \(0.729030\pi\) | |||||||
\(858\) | 3.35801e8 | − | 1.14328e8i | 0.531642 | − | 0.181005i | ||||
\(859\) | −9.74495e8 | −1.53745 | −0.768724 | − | 0.639581i | \(-0.779108\pi\) | ||||
−0.768724 | + | 0.639581i | \(0.779108\pi\) | |||||||
\(860\) | 5.68591e8i | 0.893933i | ||||||||
\(861\) | 6.63810e7 | + | 1.94972e8i | 0.104000 | + | 0.305466i | ||||
\(862\) | 3.79468e8 | 0.592452 | ||||||||
\(863\) | − | 6.87704e8i | − | 1.06996i | −0.844864 | − | 0.534982i | \(-0.820318\pi\) | ||
0.844864 | − | 0.534982i | \(-0.179682\pi\) | |||||||
\(864\) | 4.40821e8 | + | 2.92819e8i | 0.683473 | + | 0.454003i | ||||
\(865\) | 1.18134e9 | 1.82526 | ||||||||
\(866\) | − | 3.12790e8i | − | 0.481614i | ||||||
\(867\) | −3.10938e8 | + | 1.05863e8i | −0.477108 | + | 0.162438i | ||||
\(868\) | −7.69083e7 | −0.117602 | ||||||||
\(869\) | 8.91083e8i | 1.35787i | ||||||||
\(870\) | −1.27072e8 | − | 3.73233e8i | −0.192971 | − | 0.566790i | ||||
\(871\) | −3.95383e8 | −0.598361 | ||||||||
\(872\) | − | 2.41618e8i | − | 0.364401i | ||||||
\(873\) | −8.24583e7 | + | 6.35099e7i | −0.123934 | + | 0.0954550i | ||||
\(874\) | 8.53875e8 | 1.27897 | ||||||||
\(875\) | − | 1.94108e8i | − | 0.289748i | ||||||
\(876\) | 3.68887e7 | − | 1.25593e7i | 0.0548758 | − | 0.0186832i | ||||
\(877\) | −1.03427e8 | −0.153333 | −0.0766667 | − | 0.997057i | \(-0.524428\pi\) | ||||
−0.0766667 | + | 0.997057i | \(0.524428\pi\) | |||||||
\(878\) | 2.92807e8i | 0.432611i | ||||||||
\(879\) | −1.20741e8 | − | 3.54637e8i | −0.177782 | − | 0.522177i | ||||
\(880\) | −3.58474e8 | −0.526029 | ||||||||
\(881\) | − | 8.22218e8i | − | 1.20243i | −0.799088 | − | 0.601214i | \(-0.794684\pi\) | ||
0.799088 | − | 0.601214i | \(-0.205316\pi\) | |||||||
\(882\) | 4.42737e7 | + | 5.74829e7i | 0.0645268 | + | 0.0837786i | ||||
\(883\) | −1.21358e9 | −1.76273 | −0.881365 | − | 0.472436i | \(-0.843375\pi\) | ||||
−0.881365 | + | 0.472436i | \(0.843375\pi\) | |||||||
\(884\) | 2.19453e8i | 0.317676i | ||||||||
\(885\) | 6.69005e8 | − | 2.27772e8i | 0.965160 | − | 0.328602i | ||||
\(886\) | −6.67827e8 | −0.960203 | ||||||||
\(887\) | − | 1.73496e8i | − | 0.248610i | −0.992244 | − | 0.124305i | \(-0.960330\pi\) | ||
0.992244 | − | 0.124305i | \(-0.0396701\pi\) | |||||||
\(888\) | 4.05556e7 | + | 1.19119e8i | 0.0579177 | + | 0.170114i | ||||
\(889\) | 3.09788e8 | 0.440919 | ||||||||
\(890\) | − | 7.05440e8i | − | 1.00067i | ||||||
\(891\) | 9.05505e8 | + | 2.39120e8i | 1.28014 | + | 0.338051i | ||||
\(892\) | 6.34698e7 | 0.0894278 | ||||||||
\(893\) | − | 2.63069e8i | − | 0.369415i | ||||||
\(894\) | −3.27911e8 | + | 1.11642e8i | −0.458926 | + | 0.156248i | ||||
\(895\) | −1.02635e9 | −1.43161 | ||||||||
\(896\) | 3.16957e7i | 0.0440632i | ||||||||
\(897\) | −1.68498e8 | − | 4.94906e8i | −0.233462 | − | 0.685718i | ||||
\(898\) | −1.87148e8 | −0.258439 | ||||||||
\(899\) | 3.49826e8i | 0.481474i | ||||||||
\(900\) | −8.79905e7 | + | 6.77709e7i | −0.120700 | + | 0.0929642i | ||||
\(901\) | −7.57905e8 | −1.03619 | ||||||||
\(902\) | − | 6.14063e8i | − | 0.836745i | ||||||
\(903\) | −4.50551e8 | + | 1.53396e8i | −0.611900 | + | 0.208330i | ||||
\(904\) | 7.18874e8 | 0.973078 | ||||||||
\(905\) | 1.00053e9i | 1.34985i | ||||||||
\(906\) | 2.23578e8 | + | 6.56687e8i | 0.300639 | + | 0.883026i | ||||
\(907\) | 1.29528e9 | 1.73596 | 0.867982 | − | 0.496595i | \(-0.165416\pi\) | ||||
0.867982 | + | 0.496595i | \(0.165416\pi\) | |||||||
\(908\) | − | 3.49888e8i | − | 0.467381i | ||||||
\(909\) | −2.92123e8 | − | 3.79278e8i | −0.388932 | − | 0.504971i | ||||
\(910\) | −1.39696e8 | −0.185378 | ||||||||
\(911\) | 1.89887e8i | 0.251153i | 0.992084 | + | 0.125577i | \(0.0400781\pi\) | ||||
−0.992084 | + | 0.125577i | \(0.959922\pi\) | |||||||
\(912\) | 3.37220e8 | − | 1.14811e8i | 0.444559 | − | 0.151356i | ||||
\(913\) | −6.01848e8 | −0.790815 | ||||||||
\(914\) | − | 5.01268e8i | − | 0.656494i | ||||||
\(915\) | −3.78193e8 | − | 1.11082e9i | −0.493685 | − | 1.45004i | ||||
\(916\) | 1.26304e8 | 0.164335 | ||||||||
\(917\) | − | 2.74758e8i | − | 0.356322i | ||||||
\(918\) | 3.88589e8 | − | 5.84996e8i | 0.502299 | − | 0.756180i | ||||
\(919\) | −9.32821e8 | −1.20185 | −0.600927 | − | 0.799304i | \(-0.705202\pi\) | ||||
−0.600927 | + | 0.799304i | \(0.705202\pi\) | |||||||
\(920\) | 1.22342e9i | 1.57113i | ||||||||
\(921\) | −5.46630e7 | + | 1.86108e7i | −0.0699705 | + | 0.0238224i | ||||
\(922\) | −6.75197e8 | −0.861465 | ||||||||
\(923\) | 5.51631e8i | 0.701526i | ||||||||
\(924\) | 5.75186e7 | + | 1.68942e8i | 0.0729109 | + | 0.214152i | ||||
\(925\) | −4.45949e7 | −0.0563456 | ||||||||
\(926\) | 6.70587e8i | 0.844544i | ||||||||
\(927\) | 4.46560e8 | − | 3.43944e8i | 0.560584 | − | 0.431766i | ||||
\(928\) | 4.58705e8 | 0.573970 | ||||||||
\(929\) | 8.77845e7i | 0.109489i | 0.998500 | + | 0.0547445i | \(0.0174344\pi\) | ||||
−0.998500 | + | 0.0547445i | \(0.982566\pi\) | |||||||
\(930\) | −4.48584e8 | + | 1.52727e8i | −0.557693 | + | 0.189874i | ||||
\(931\) | −1.57562e8 | −0.195255 | ||||||||
\(932\) | 2.01882e8i | 0.249373i | ||||||||
\(933\) | −1.91830e8 | − | 5.63436e8i | −0.236195 | − | 0.693745i | ||||
\(934\) | 8.60700e7 | 0.105636 | ||||||||
\(935\) | − | 1.53470e9i | − | 1.87754i | ||||||
\(936\) | −3.08190e8 | − | 4.00140e8i | −0.375830 | − | 0.487960i | ||||
\(937\) | −8.62672e8 | −1.04864 | −0.524320 | − | 0.851521i | \(-0.675681\pi\) | ||||
−0.524320 | + | 0.851521i | \(0.675681\pi\) | |||||||
\(938\) | 2.41113e8i | 0.292155i | ||||||||
\(939\) | 1.92387e8 | − | 6.55009e7i | 0.232370 | − | 0.0791135i | ||||
\(940\) | 1.17343e8 | 0.141278 | ||||||||
\(941\) | − | 1.30884e9i | − | 1.57079i | −0.618998 | − | 0.785393i | \(-0.712461\pi\) | ||
0.618998 | − | 0.785393i | \(-0.287539\pi\) | |||||||
\(942\) | 2.73364e8 | + | 8.02916e8i | 0.327030 | + | 0.960544i | ||||
\(943\) | −9.05012e8 | −1.07924 | ||||||||
\(944\) | − | 2.54863e8i | − | 0.302964i | ||||||
\(945\) | −3.07218e8 | − | 2.04073e8i | −0.364042 | − | 0.241818i | ||||
\(946\) | 1.41900e9 | 1.67614 | ||||||||
\(947\) | 8.66006e8i | 1.01970i | 0.860264 | + | 0.509848i | \(0.170298\pi\) | ||||
−0.860264 | + | 0.509848i | \(0.829702\pi\) | |||||||
\(948\) | 3.73906e8 | − | 1.27301e8i | 0.438871 | − | 0.149420i | ||||
\(949\) | −6.28023e7 | −0.0734813 | ||||||||
\(950\) | 2.92345e8i | 0.340977i | ||||||||
\(951\) | 9.64262e7 | + | 2.83220e8i | 0.112112 | + | 0.329293i | ||||
\(952\) | 4.29871e8 | 0.498227 | ||||||||
\(953\) | 2.34543e8i | 0.270984i | 0.990778 | + | 0.135492i | \(0.0432615\pi\) | ||||
−0.990778 | + | 0.135492i | \(0.956738\pi\) | |||||||
\(954\) | 4.30222e8 | − | 3.31360e8i | 0.495504 | − | 0.381640i | ||||
\(955\) | −7.48215e8 | −0.859045 | ||||||||
\(956\) | − | 3.79201e8i | − | 0.434006i | ||||||
\(957\) | 7.68451e8 | − | 2.61630e8i | 0.876759 | − | 0.298505i | ||||
\(958\) | −6.86858e8 | −0.781215 | ||||||||
\(959\) | − | 1.40649e8i | − | 0.159470i | ||||||
\(960\) | 3.13548e8 | + | 9.20945e8i | 0.354398 | + | 1.04093i | ||||
\(961\) | −4.67052e8 | −0.526254 | ||||||||
\(962\) | − | 6.31348e7i | − | 0.0709159i | ||||||
\(963\) | 6.46577e8 | + | 8.39486e8i | 0.724005 | + | 0.940014i | ||||
\(964\) | 1.56699e8 | 0.174918 | ||||||||
\(965\) | 1.15548e9i | 1.28582i | ||||||||
\(966\) | −3.01805e8 | + | 1.02754e8i | −0.334807 | + | 0.113990i | ||||
\(967\) | 1.11442e9 | 1.23245 | 0.616225 | − | 0.787570i | \(-0.288661\pi\) | ||||
0.616225 | + | 0.787570i | \(0.288661\pi\) | |||||||
\(968\) | − | 7.34169e8i | − | 0.809412i | ||||||
\(969\) | 4.91532e8 | + | 1.44371e9i | 0.540232 | + | 1.58675i | ||||
\(970\) | −1.22203e8 | −0.133896 | ||||||||
\(971\) | 2.30673e8i | 0.251964i | 0.992033 | + | 0.125982i | \(0.0402081\pi\) | ||||
−0.992033 | + | 0.125982i | \(0.959792\pi\) | |||||||
\(972\) | −2.90252e7 | − | 4.14119e8i | −0.0316065 | − | 0.450948i | ||||
\(973\) | −5.08762e8 | −0.552301 | ||||||||
\(974\) | 3.36273e8i | 0.363928i | ||||||||
\(975\) | 1.69443e8 | − | 5.76893e7i | 0.182814 | − | 0.0622417i | ||||
\(976\) | −4.23174e8 | −0.455166 | ||||||||
\(977\) | 6.28575e8i | 0.674021i | 0.941501 | + | 0.337011i | \(0.109416\pi\) | ||||
−0.941501 | + | 0.337011i | \(0.890584\pi\) | |||||||
\(978\) | 2.36361e8 | + | 6.94232e8i | 0.252673 | + | 0.742144i | ||||
\(979\) | 1.45243e9 | 1.54792 | ||||||||
\(980\) | − | 7.02813e7i | − | 0.0746726i | ||||||
\(981\) | −2.53570e8 | + | 1.95301e8i | −0.268591 | + | 0.206870i | ||||
\(982\) | 6.81578e7 | 0.0719749 | ||||||||
\(983\) | − | 7.03769e8i | − | 0.740917i | −0.928849 | − | 0.370458i | \(-0.879201\pi\) | ||
0.928849 | − | 0.370458i | \(-0.120799\pi\) | |||||||
\(984\) | −8.27655e8 | + | 2.81787e8i | −0.868689 | + | 0.295757i | ||||
\(985\) | 4.91409e8 | 0.514202 | ||||||||
\(986\) | − | 6.08729e8i | − | 0.635028i | ||||||
\(987\) | 3.16572e7 | + | 9.29825e7i | 0.0329246 | + | 0.0967052i | ||||
\(988\) | 3.41454e8 | 0.354047 | ||||||||
\(989\) | − | 2.09134e9i | − | 2.16190i | ||||||
\(990\) | 6.70979e8 | + | 8.71168e8i | 0.691518 | + | 0.897834i | ||||
\(991\) | 3.96582e8 | 0.407485 | 0.203743 | − | 0.979025i | \(-0.434689\pi\) | ||||
0.203743 | + | 0.979025i | \(0.434689\pi\) | |||||||
\(992\) | − | 5.51312e8i | − | 0.564758i | ||||||
\(993\) | −8.05964e8 | + | 2.74402e8i | −0.823129 | + | 0.280246i | ||||
\(994\) | 3.36397e8 | 0.342526 | ||||||||
\(995\) | 1.05020e9i | 1.06611i | ||||||||
\(996\) | 8.59810e7 | + | 2.52541e8i | 0.0870211 | + | 0.255596i | ||||
\(997\) | 7.57185e8 | 0.764041 | 0.382020 | − | 0.924154i | \(-0.375228\pi\) | ||||
0.382020 | + | 0.924154i | \(0.375228\pi\) | |||||||
\(998\) | 5.79708e8i | 0.583200i | ||||||||
\(999\) | 9.22296e7 | − | 1.38846e8i | 0.0925068 | − | 0.139263i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 21.7.b.a.8.8 | yes | 12 | |
3.2 | odd | 2 | inner | 21.7.b.a.8.5 | ✓ | 12 | |
4.3 | odd | 2 | 336.7.d.a.113.4 | 12 | |||
7.6 | odd | 2 | 147.7.b.b.50.8 | 12 | |||
12.11 | even | 2 | 336.7.d.a.113.3 | 12 | |||
21.20 | even | 2 | 147.7.b.b.50.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.7.b.a.8.5 | ✓ | 12 | 3.2 | odd | 2 | inner | |
21.7.b.a.8.8 | yes | 12 | 1.1 | even | 1 | trivial | |
147.7.b.b.50.5 | 12 | 21.20 | even | 2 | |||
147.7.b.b.50.8 | 12 | 7.6 | odd | 2 | |||
336.7.d.a.113.3 | 12 | 12.11 | even | 2 | |||
336.7.d.a.113.4 | 12 | 4.3 | odd | 2 |